1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ArbitrLikvidat [17]
3 years ago
14

The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play

ed the course today. Find the probability that the average score of the 64 golfers exceeded 76. Round to four decimal places.
Mathematics
1 answer:
Vilka [71]3 years ago
6 0

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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

Z = \frac{X - \mu}{\sigma}

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 \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

In this problem, we have that:

\mu = 75, \sigma = 4, n = 64, s = \frac{4}{\sqrt{64}} = 0.5

Find the probability that the average score of the 64 golfers exceeded 76.

This is 1 subtracted by the pvalue of Z when X = 64.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{76 - 75}{0.5}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

You might be interested in
What is the slope of the linear equation y=x+10
Anettt [7]

Answer:

slope = 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 10 ← is in slope- intercept form

with slope m = 1

5 0
2 years ago
Read 2 more answers
Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue
Murljashka [212]

Answer: 1. 7:10

2. 10 blue cans

15 yellow cans.

3. 4 cans of blue paint.

5 cans of yellow paint.

4. 2 blue cans and 3 yellow cans.

Step-by-step explanation:

1. 14 blue paint cans/20 yellow paint cans=

14/20=

7/10 ==> 7:10

2. 4+6 blue cans=10 blue cans

6+9 yellow cans=15 yellow cans.

3. 14-10=4 cans of blue paint.

20-15=5 cans of yellow paint.

4. 10 blue cans/15 yellow cans=

10/15=

2/3 ==> 2:3 ==> 2 blue cans and 3 yellow cans.

5 0
9 months ago
Read 2 more answers
REALLY NEED HELP:  The Venn Diagram shows a universe with 26 elements and two different outcomes: B and Y
Goshia [24]

Answer:

P(B|Y)=0.4

Step-by-step explanation:

We are given with a Venn diagram of a universe with 26 elements and two different outcomes: B and Y

And we are asked to find P(B|Y)

The formula for P(B|Y)= \frac{P(B\cap Y)}{P(Y)}

From Venn diagram, P(B\cap Y)=\frac{n(B\cap Y)}{26} =\frac{8}{26} =\frac{4}{13}

And P(Y)=\frac{n(Y)}{26}=\frac{8+12}{26}= \frac{20}{26}= \frac{10}{13}

Hence P(B|Y)=\frac{(\frac{4}{13})}{\frac{10}{13}} =\frac{4}{10}=0.4

6 0
3 years ago
Read 2 more answers
Which pair of the following tests is used to test for normality?
marissa [1.9K]

Answer: the answer is b( a quantile - quantile plot and a p- value test

Step-by-step explanation:

8 0
2 years ago
find the present and future value of $1000 received every month end for 20 years if the interest rate is j12=12%p.a
GenaCL600 [577]

Answer:

asasassasas

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Dan made $242 for 11 hours of work.
    6·1 answer
  • . Alexandro, o professor de Física, avisou aos alunos que a média bimestral seria calculada conforme o seguinte critério: Adicio
    10·1 answer
  • Anna's hair is 24 inches long. This is 12 inches longer than her
    13·2 answers
  • Which function represents exponential decay?
    8·2 answers
  • Same points yall<br> 5+4x x=8
    13·1 answer
  • What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?
    7·1 answer
  • PLEEEEASSEEEEE ITS URGENT
    14·1 answer
  • Help me please!!!!!!!!!
    7·1 answer
  • The sum of two rational numbers is -8. if one of the is -8/17, find the other. plz help me ​
    9·2 answers
  • Marcella is flying a kite in a competition. To win the competition, her kite string must have at least 162 feet released. The ki
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!