The amount of time all students in a very large undergraduate statistics course take to complete an examination is distributed continuously and normally. The probability a student selected at random takes at least 55.50 minutes to complete the examination equals 0.6915. The probability a student selected at random takes no more than 71.52 minutes to complete the examination equals 0.8997.
a) Determine the value for the mean (u) of the associated distribution
b) Determine the value for the standard deviation (o) of the associated distribution.

Answer:

a) The mean is [tex]\mu = 60[/tex]

b) The standard deviation is [tex]\sigma = 9[/tex]

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using 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.

The probability a student selected at random takes at least 55.50 minutes to complete the examination equals 0.6915.

This means that when X = 55.5, Z has a pvalue of 1 - 0.6915 = 0.3085. This means that when [tex]X = 55.5, Z = -0.5[/tex]

So

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

[tex]-0.5 = \frac{55.5 - \mu}{\sigma}[/tex]

[tex]-0.5\sigma = 55.5 - \mu[/tex]

[tex]\mu = 55.5 + 0.5\sigma[/tex]

The probability a student selected at random takes no more than 71.52 minutes to complete the examination equals 0.8997.

This means that when X = 71.52, Z has a pvalue of 0.8997. This means that when [tex]X = 71.52, Z = 1.28[/tex]

So

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

[tex]1.28 = \frac{71.52 - \mu}{\sigma}[/tex]

[tex]1.28\sigma = 71.52 - \mu[/tex]

[tex]\mu = 71.52 - 1.28\sigma[/tex]

Since we also have that [tex]\mu = 55.5 + 0.5\sigma[/tex]

[tex]55.5 + 0.5\sigma = 71.52 - 1.28\sigma[/tex]

[tex]1.78\sigma = 71.52 - 55.5[/tex]

[tex]\sigma = \frac{(71.52 - 55.5)}{1.78}[/tex]

[tex]\sigma = 9[/tex]

[tex]\mu = 55.5 + 0.5\sigma = 55.5 + 0.5*9 = 55.5 + 4.5 = 60[/tex]

Question

The mean is [tex]\mu = 60[/tex]

The standard deviation is [tex]\sigma = 9[/tex]

The linear function f(x) = 0 5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function 9(x) represents the average test score in your science
class, where x is the number of the test taken.
x 0x)
1 81
283
3 85
Part A: Determine the test average for your math class after completing test 2.
Part B: Determine the test average for your science class after the completing test 2.
Part C: Which class had a higher average after completing test 4? Show work to support your answer

3. A deli sells small, medium, and large box lunches. Each can of soda costs $1 and each bag of chips costs $1. Each sandwich costs s dollars. Some customers buy box lunches, and some customers buy items separately. Use this and the information below to solve Parts A, B, and C.

• Michelle buys 6 sandwiches and 2 sodas. Her total cost is 6s+ 2.

• Beyunka buys 6 small box lunches. These box lunches include 1 sandwich, 1 soda, and 1 bag of chips. Her total cost is 6(s + 2).

Duff buys 3 medium box lunches. These box lunches do not include soda. His total cost is 3(2s + 3).

3. PART A: Each medium box lunch purchased by Duff contains two sandwiches and three bags of chips. If sandwiches cost $7.75, what is Duff's total cost? ​

Can someone please solve this for me?

107 + 12

Show your work and I'll give brianliest (I know the answer i just need someone to show their work on how to get it)

there are 4 red balls in a bag and 8 yellow balls a ball is drawn random from the bag find the probability of not red ball​

slove this plzzz plzzz​

A basketball player makes 85% of her foul shots. If 10 of her foul shots are randomly selected, what is the probability that 8 of them are successful shots?
0.06
0.28
0.85
0.98

Complete the statement. Round to the nearest hundredth if necessary. 48 ft =_____yd​

What is the answer to this

When bivariate data from a survey is graphed what is graph called ?

Simplify the expression below. A. 83 B. 812 C. 84 D. 88

Need help Arc angles

can someone please help me i cant fail this

CAN SOMEONE HELP ME PLZZZ

(8x+1/2x) raise to a power of 8

giving brainliest !! *easy*

If 4x - 3y = -18 and 6x + 7y = -4, then what is the value of y?

20. Find the mean, median, and mode for the following
data set:
83 98 22 89 99 98

I'm lost on this please help

A scuba diver is at an elevation of 53 feet below sea level. A hiker is at an elevation of 228 feet above sea level. What is the difference in elevation between the scuba diver and the hiker?

There is a sale on sneakers. The price tag says $150. There is a 25% off sale. What is the final price with the discount? USE AN EXPRESSION.
Expression: ___________________
Answer:_______________________

-4x - 4(6x-14) +8(6x-10) - (20x -18)

Researchers wanted to know if people, on average, tend to underestimate the duration of a typical cold. Clinical literature reports that the actual duration of a typical cold is roughly 15 days. The researchers surveyed a random sample of 352 healthy adults and asked them how long they think that a typical cold lasts. The results of this survey were that the average time that the 352 people thought a cold lasts was two weeks (14 days) with a standard deviation of 0.5 days. So, according to this survey, do people tend to underestimate the duration of a cold (with statistical significance)?

can someone help please?;)

Find the third degree polynomial function that has an output of 40 when x=1, and has zeros −19 and −i?

Solve for x in terms of h.
10x + 20h = -4(-3x - 8h)

A perfect square is the product of any positive whole number used as a factor exactly two times. [Example: 49 is a perfect square because 7 × 7 = 49] … The positive whole number N, when multiplied by 150, is a perfect square.

a consumer is constrained by
​

if a football team played 160 matches and won 65 percent of them,how many matches did it win​

Look at the figure. Which point is coplanar with points B, C, and H?

PLEASE HELP ASAP!!

k= y/x (3x-1)-2.75(x+2)