In order to study the relationship between playing football and traumatic brain injuries, researchers placed accelerometers in the helmets of many high school football teams. Accelerometers measure the amount of hits that boys playing high school football absorb during a season. Suppose the average number of hits absorbed by a helmet during a season was 355 hits with a standard deviation of 80 hits. What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits

Answers

Answer 1

Answer:

56.96% probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a single player:

[tex]\mu = 355, \sigma = 80[/tex]

For the sample mean(of 48 playes).

[tex]n = 48, s = \frac{80}{\sqrt{48}} = 11.547[/tex]

What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits?

This is the pvalue of Z when X = 360 subtracted by the pvalue of Z when X = 340. So

X = 360

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{360 - 355}{11.547}[/tex]

[tex]Z = 0.43[/tex]

[tex]Z = 0.43[/tex] has a pvalue of 0.6664

X = 340

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{340 - 355}{11.547}[/tex]

[tex]Z = -1.30[/tex]

[tex]Z = -1.30[/tex] has a pvalue of 0.0968

0.6664 - 0.0968 = 0.5696

56.96% probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits


Related Questions

You can buy five cans for green beans at the village market for $2.20 you can buy 10 of the same cans of beans at Sam’s Club for $5.30 which place is better

Answers

Answer:

The village market is better than Sam's Club

Step-by-step explanation:

If you buy 5 more cans of green beans at the village, it will cost $4.40 in total. Therefore if you go buy the beans at Sam's club, the village one will be cheaper.

Which expression is equivalent to 21^3sqrt15 - 9^3sqrt15?

A. 12
B. 30^3sqrt15
C. 12^3sqrt5
D. 12^3sqrt15

Answers

Answer:

the answer is D.

Step-by-step explanation:

Since the square: (3√15) is common in both of them, you only focus on 21 and 9. if you subtract 9 from 21, it will give you 12. so, just add (3√15) to 12, which will give you: 12^3sqrt15

Help! It’s due it’s due in 30 minutes

Answers

the area would be
36+18+18+4+4+4+4=16+72=88

Answer:

Contains two 6x6 triangles, contains one 12x3 rectangle, four 2x2 triangles, and two 2x2 squares.

88

Step-by-step explanation:

You only need the area of one side of this shape to find the total area.

((6*6)/2+(3*6)+(2*2)+(2*2))2 = 88. What's inside the parenthesis is the area for one side of the shape, then you can multiply that by two to get the entire area.

1.2.
Prove the following the trigonometric identity step-by-step
1.2.1 sin theta/sin theta+cos theta=tan theta/1+tan theta​

Answers

Answer:

The identity is proved below.

Step-by-step explanation:

The tangent of an angle [tex]\theta[/tex] is given by:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

In this question, we are given the following trigonometric identity:

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\tan{\theta}}{1+\tan{\theta}}[/tex]

Applying the tangent

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{1+\frac{\sin{\theta}}{\cos{\theta}}}[/tex]

Now, we apply the least common multiple on the denominator. So

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{\frac{\cos{\theta}+\sin{\theta}}{\cos{\theta}}}[/tex]

SImplifying the cosine:

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}}[/tex]

Which means that the identity is proved.

What is the surface area of the rectangular prism?

PLSSS HELP GUYS I NEED HELP ASAP

Answers

Answer:

348 ignore this eoendndisiwjd

In 2009, two tickets to a certain American band's concert and two tickets to a certain British band's concert cost, on average, a total of $592. At those prices, four tickets to see this
American band and two tickets to see this British pand cost $842. What was the average cost of these American and British band tickets in 2009?
American band $
British band$

Answers

I believe you would divide

There are 946 milliliters in a quart. There are 2 pints in a quart
How many milliliters are in a pint?

Answers

Answer:

There are 473 millimeters in 1 pint.

Step-by-step explanation:

946 ml in 1 quart.

2 pints in 1 quart

hence,

946 ml in 2 pints

hence in 1 pint we have 946/2 ml

i.e. 473 ml in 1 pint.

:)

Answer:

473 milliliters

Step-by-step explanation:

If there are 946 mL in a quart and there are 2 pints in a quart, divide 946 by 2 to find how many mL are in one pint.

Here's an equation you can set up to solve the problem.

— 946 = 2x

— 946 / 2 = 2x / 2

— 473 = x

So, if we let x stand for the amount of mL in a pint, then 473 = x means there are 473 mL in a pint.

Please help me answer this will give brainlst

Answers

Answer:

17° and 73°

Step-by-step explanation:

For two complementary angles, the sum of angles is equal to 90 degrees.

Let other angles = x

First angle = 5+4x ...(1)

ATQ,

5+4x+x=90 ...(2)

Equation (1) and (2) shows the equations for the given problems.

5+5x=90

5x = 85

x = 17°

Other angle = 17

First angle = 5+4x

= 5+4(17)

= 73°

So, the other two angles are 17° and 73° respectively.

question 2, thanks for the help :)

Answers

Answer:

the slope of the line passing through (4, 4)  and (9, 1)   is:

Slope = -3/5

Step-by-step explanation:

Given the points on the graph

(4, 4)(9, 1)

Here:

(x₁, y₁) = (4, 4)

(x₂, y₂) = (9, 1)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [1 - 4] / [9 - 4]

               = -3 / 5

Thus, the slope of the line passing through (4, 4)  and (9, 1)   is:

Slope = -3/5

Each diagram is made of smaller, identical pieces. Tell how many pieces you would shade to model 25%

Answers

Answer:

12 pieces

Step-by-step explanation:

AE = 3x - 2 and EC = 2x + 3 then DB =

#5

Answers

Answer:

DB = 26

Step-by-step explanation:

Remember:

AE ≅ ECAC ≅ DB

☆The equation in finding the value of x would be 3x - 2 = 2x + 3.

☆Let's solve the equation.

[tex] \: \: \: \: \: \: \: \: \: 3x - 2 = 2x + 3 \\ \frac{ - 2x \: \: \: \ = - 2x}{x - 2 = 3} \\ \frac{ \: \: \: \: \: + 2 = + 2}{x = 5} [/tex]

☆Now that we found the value of x, we are going to plug in for AE and EC.

[tex]AE ; \\ 3x - 2 \\ 3(5) - 2 \\ 15 - 2 \\ 13 \\ \\ \\ \\ and \\ \\ \\ \\ \\ EC; \\ 2x + 3 \\ 2(5) + 3 \\ 10 + 3 \\ 13[/tex]

☆AE and EC each measure 13. To find the length of AC, you will have to add AE and EC. [tex]13 + 13 = 26[/tex]

The length of AC is 26. And since we know that AC is congruent (equal) to DB, meaning they measure the same. DB length is also 26.

What is the value of x

Answers

Answer:

54

Step-by-step explanation:

c)
How many quarters make a whole?
d) How many fifths make a whole?
e) How many tenths make a whole?
nta Excel in Mathematics - Book 3
108​

Answers

Answer:

4 quarters

10 tenths

Step-by-step explanation:

Tenths

[tex] \frac{1}{10} [/tex]

Quarter

[tex] \frac{1}{4} [/tex]

Whole

[tex] 1 [/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex] 1 = \frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4} [/tex]

∴ There are 4 quarters to make a whole

[tex] 1 = \frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10} [/tex]

∴ There are 10 tenths to make a whole

Find the length of dm in the given fig.​

Answers

Answer:

[tex]DM=12[/tex]

Step-by-step explanation:

(Let the point where the altitude from [tex]D[/tex] intersects [tex]AB[/tex] be called as point [tex]E[/tex].) First, let's find the area of parallelogram [tex]ABCD[/tex]. The area of a parallelogram is simply [tex]b*h=bh[/tex], where [tex]b[/tex] is the parallelogram's base and [tex]h[/tex] is the parallelogram's height. If we let [tex]AB[/tex] and [tex]DE[/tex] be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram [tex]ABCD[/tex] will be [tex]AB*DE=15*8=120[/tex].

Now, how does this information matter, you might ask? Well, we can take either [tex]AB[/tex] or [tex]CB[/tex] to be the base and either [tex]DE[/tex] or [tex]DM[/tex] to be the height. In this case, let's take the latter two options, as we are looking to find the length of [tex]DM[/tex].

Therefore, we know that the area of parallelogram [tex]ABCD[/tex] can also be found by calculating [tex]CB*DM[/tex]. Since we know the values of the area and [tex]CB[/tex], we can write the following equation to solve for [tex]DM[/tex]:

[tex]Area = CB*DM[/tex]

[tex]120=10*DM[/tex] (Substitute [tex]Area=120[/tex] and [tex]CB=10[/tex] into the equation)

[tex]\frac{120}{10}=\frac{10*DM}{10}[/tex] (Divide both sides of the equation by [tex]10[/tex] to get rid of [tex]DM[/tex]'s coefficient)

[tex]12=DM[/tex] (Simplify)

[tex]DM=12[/tex] (Symmetric Property of Equality)

Hope this helps!


I NEED HELLPPPPPPPP

Answers

Answer:

51 people

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

190 out of 300 is from England

100 out of 100×190/300 is from England

=63% (approximately)

according to the question

63%×80

63/100 × 80

51(approximately)

find x in the proportion x:6= 25:5​

Answers

Step-by-step explanation:

[tex] \frac{x}{6} = \frac{25}{5} \\ [/tex]

[tex] \frac{x}{6} = \frac{5}{1} \\ [/tex]

[tex]x = 30[/tex]

15% of the skittles in andys bag are green. how many skittles are in the bag if 9 of them are green

Answers

Answer:

60

Step-by-step explanation:

9/15=0.6

0.6x100=60

sally is taking a test
when she got her score it was 85% of 100% how many questions was on the test and how many did she get wrong

Answers

Answer:

There was 20 questions on the test.

She got 3 wrong.

Step-by-step explanation:

[tex]\frac{85}{100} = \frac{17}{20}[/tex]

20 - 17 = 3

There was 20 questions on the test.

She got 3 wrong.

Answer: There were 20 questions and she missed three.

First of all, you need to simplify 85/100.

85/100 / 5/5 = 17/20.

Now that you know how many questions were on the test, subtract 17 from 20.

20 - 17 = 3

So in conclusion, the test had 20 questions and she missed three.

But this question doesn’t have enough info to be honest, if you multiply 17/20 with any number it’s still going to be 85%.

Is 1/2 plus 5/12 greater than 1 or less than 1

Answers

Answer:

Less than 1

1/2=6/12

6/12+5/12=11/12

11/12<1

#CarryOnLearning

Make it brainliest ty

Sally earns $9.56 per hour. What is her overtime pay at time-and-a-half?

Answers

9.56/2=4.78

It’s asking for half the time to I divided it by two.

CHECK YOUR UNDERSTANDING

The Wacky Widget Company sells widgets for

$4.00 each wholesale. A local store has a

markup of $1.20.

A. What is the retail price?

B. What percent is the markup price?

Answers

Answer:

Retail price = $5.20

Percentage of mark up price = 30%

Step-by-step explanation:

Company sells $4.00 each wholesale.

Now the local store which is the retailer has a markup of $1.20.

This means that the retail price is;

Retail price = wholesale price + mark up = $4.00 + $1.20

Retail price = $5.20

To find the percentage of the markup, it is the fraction of the wholesale price multiplied by 100%.

Thus;

Percentage of Markup is;

1.2/4 × 100% = 30%

The table shows how many slices of cake were sold during the week. Each slice of cake is equivalent to 116 of a cake. Determine if each statement is true by selecting Yes or No. Table showing the number of cake slices sold each day. Monday, eighty slices. Tuesday, one hundred twenty slices. Wednesday, one hundred slices. Thursday, one hundred forty slices. A On Monday, the restaurant made 8 cakes and will have 3 left over because −116(80)=−5. Yes No B On Tuesday, the restaurant only needed 7 cakes because −116(120)=−712. Yes No C On Wednesday, the restaurant made 7 cakes and will have 34 of a cake left over because −116(100)=−6.25. Yes No D On Thursday, the restaurant made 8 cakes and will have 34 of a cake left because −116(110)=−8.75. Yes No brainiest

Answers

Answer:

yes

no

yes

no

hope this helps

Answer:

1. Yes

2. No

3.Yes

4.No

Step-by-step explanation:

I did the test and got it right!

Add 2/7 + 3/7?
[tex]2 \7 + 3 \7[/tex]

Answers

5/7
I hope that’s what your looking for

Can someone help me out pls?

Answers

Answer:

58 degrees

Step-by-step explanation:

Jennifer uses a coupon that gives you 20% off your order. If the total was $18 before the discount, then how much money did she save?

Answers

She would have saved $3.60

Solve
12 (8 – 4) =
Q 42
o 144
102
48

Answers

Your answer will be 48.
The answer is 48 :))))

what is th eqivalent expression for 4x 2/3

Answers

Answer:

x in (-oo:+oo)

(4*x^2)/3 = 0

4/3*x^2 = 0 // : 4/3

x^2 = 0

x = 0

x = 0

Doug had a total of $75 to buy 3 pictures for his room. He paid the same amount for each picture and had $27 left over. How much money did Doug pay for each
picture?

Answers

Around 16 dollars. 75-27=48. 48/3=16

y=$1.25x + $5.00 what is the total cost of service for the month if you stream 5 videos

Answers

Answer: $11.25

Step-by-step explanation:

Answer:

$11.25

Step-by-step explanation:

I assume that x = the 5 videos streamed

5*1.25=6.25

6.25+5 =11.25

y=$11.25

A data set has a mean of 80. The value 83 lies one standard deviation above the mean. What is the margin of error?

Answers

Answer:

3

Step-by-step explanation:

Answer:

it will be 6

Step-by-step explanation:

The standard deviation is 83 – 80 = 3.  Since margin of error is two times the standard deviation, it must equal 6.

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