Two brothers, Michael and Alan, were in a bowling league that met once a
week. From past experiences, it is known that both brothers' scores are
approximately normally distributed where Michael has a mean score of 150
with a standard deviation of 30, and Alan has a mean score of 165 with a
standard deviation of 15. Assuming that their scores are independent, which
of the following values is closest to the probability that Michael will have a
greater core than Alan in a single game?
0.16
0.28
0.31
0.33
0.37

Answer:

The correct option is;

0.28

Step-by-step explanation:

The given parameters are;

The mean score for Michael, [tex]\bar x _1[/tex] = 150

The standard deviation, σ₁ = 30

The mean score for Alan,  [tex]\bar x _2[/tex] = 165

The standard deviation, σ₂ = 15

Taking n₁ = n₂ = 1

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Taking μ₁ - μ₂ = 0

[tex]z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577[/tex]

The p-value for a z-score of -0.577 from the z-table is 0.28434

Therefore, the probability that Michael, with mean score, [tex]\bar x _1[/tex] = 150 will have a greater score than Alan, with a mean score of [tex]\bar x _2[/tex] = 165 is 0.28434 ≈ 0.28

Therefore, the correct option is 0.28

Write an equation of the line that passes through (-4,3) and (0,6
)

Find the original ordered pairs.

At a real estate​ agency, an agent sold a house for ​$396,000. The commission rate is ​7.5% for the real estate agency and the commission rate for the agent is ​20% of the amount the real estate agency gets. How much did the agency make on the​ house? How much did the agent earn in​ commission?

Write an equation to represent the table. (1 point)

Boxes of Candy
5
7
9
Pieces of Candy
80
112
144

Question 24 (1 point)
Which of the following is NOT a Congruence Postulate/Theorem
SSS
4
АА
SAS
ASA

An 8-column table with 14 rows titled Table 1, Employment by major industry sector, 1996, 2006, and projected 2016. Column 1 is labeled Industry sector with entries services-providing, utilities, wholesale trade, retail trade, transportation and warehousing, information, financial activities, professional and business services, educational services, health care and social assistance, leisure and hospitality, other services, federal government, state and local government. Column 2 is thousands of jobs in 1996 with entries 97,042.9, 639.5, 5,522.1, 14,142.6, 3,935.5, 2,940, 6,968.6, 13,461.8, 2,077.5, 11,604.8, 10,776.5, 5,434.9, 2,877, 16,662.1. Column 3 is labeled thousands of jobs in 2006 with entries 114,407.3, 548.5, 5,897.7, 15,319.4, 4,465.8, 3,054.9, 8,363.2, 17,551.6, 2,918.4, 14,919.8, 13,143.4, 6,234.6, 2,728.3, 19,261.7. Column 4 is labeled thousands of jobs in 2016 with entries 130,189.7, 517.6, 6,326.2, 16,006.4, 4,962, 3,266.7, 9,570.1, 21,643.7, 3,527.4, 18,954.1, 15,016.7, 7,077.2, 2,625.7, 20,696.1. Column 5 is labeled Numeric change 1996 to 2006 with entries 17,354.4, negative 91, 375.6, 1,176.8, 530.3, 114.9, 1,394.6, 4,089.8, 840.9, 3,315, 2,366.9, 799.7, negative 148.7, 2,599.6. Column 6 is labeled numeric change 2006 to 2016 with entries 15,782.4, negative 30.9, 428.5, 687, 496.2, 211.8, 1,206.9, 4,092.1, 609, 4,034.3, 1,873.3, 842.6, negative 102.6, 1,434.4. Column 7 is labeled Average annual rate of change, 1996 to 2006 with entries 1.7, negative 1.5, .7, .8, 1.3, .4, 1.8, 2.7, 3.5, 2, 1.4, negative .5, 1.5. Column 8 is labeled average annual rate of change, 2006 to 2016 with entries 1.3, negative .6, .7, .4, 1.1, .7, 1.4, 2.1, 1.9, 2.4, 1.3, 1.3, negative .4, .7. Based on the above chart, which industry’s average annual rate of change is projected to decrease the most in the 2006-2016 period as compared to its average annual rate of change during 1996-2006? a. Utilities b. Educational services c. Federal government d. State and local government

Find the 52nd term of the arithmetic sequence-8, -12, -16,...

Please help! I’ll mark brainlist and 5 stars!

(You have to see which one is right for the sentence provided, and which ones are false out of A-D)

A. The equation of the line is y = 1/2x

B. Sasha can make 60 gift bags in 2 hours.

C. The constant of proportionality is l = 1/2

D. Sasha can make 2 bags per minute.

CAN SOMEONE ASAP HELP ME PLEASE

help. answer is not D

for geometry help thanks <33

4x^3(5x) = what,
will mark brainliest

plz help it’s the pythagorean theorem

pls helppp
math work
bleh

Solve: 7n + 5 = -44 HELPPPPPPPPPPP

-3/4-5/8=
This is a simple math problem
But it’s to hard for me
And I really need help
Not from someone who doesn’t know the answer

Someone please help me I’m struggling rn

I'll give 15 points for this question ​

pls help :( i’ll give brainliest

Find the slope of the line.

I WILL MARK BRAINYLIST JUST HELP MEEE

a boat used 1/24 of a gallon of gas to drive 1/3 of a mile.At this rate how many miles can the boat go using 1 gallon of gas.

pls help me solve this

If the height of Mount Everest is about 8.8 time 10 to the third power meters and the height of the Empire State Building is about 3.8 times 10 to the second power meters which of these statements is a true

I’ll love you forever if you help me with this ASAP PLEASE

Help please!
Thank you!

Nathan has a 16 ounce energy drink. He drinks 9 ounces. Enter the percentage of ounces Nathan has left of his energy drink. Round your answer to the nearest hundredth

Suri saved $50 of her paycheck the first week she worked and $25 of her paycheck each week after the first week.
How many weeks did it take Suri to save a total of $1,000?

The expression ( x − 12 ) is a factor of x 2 + p x − 48 . What is the value of p ?

In which quadrant is point C located

NEED ANSWER ASAP!!!!!!!!
An airplane is flying at 32,000 feet when it starts it’s decent. It is
descending at a rate of 2000 feet per minute. Let x represent the minutes
of the flights descent and y represent the plane’s altitude.

a. Fill in the table.

b. Write an equation in slope-intercept form for the plane’s altitude.
c. Graph the equation from part (b).