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
The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?
zalisa [80]
Hey there :)

The volume formula of a cylinder is:
V = \pir²h

The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first

9648 = \pir²(18)
\frac{9648}{18} = \pir²
536 = \pir²
\frac{536}{ \pi} = r²
\sqrt{ \frac{536}{ \pi } } = r
r ≈ 13.06

The ratio of the big cylinder to small cylinder is:
18 : 9   (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger

\frac{13.06}{2} = r
r ≈ 6.53  ( the radius of the small radius )

V (of small cylinder) = \pi(6.53)²(9)
                                  = 1206 in³
3 0
3 years ago
The formula c=3.14 can be used
Nataly [62]

it can be used to calculate the length of a circular bracelet

4 0
3 years ago
5. Rounded to three decimal places, what is the value of r for this data set?
IrinaVladis [17]

The value of correlation coefficient (r) for the dataset is 0.981

<h3>What is correlation coefficient (r)?</h3>

The correlation coefficient (r) is used to determine the closeness and association of a scatter plot points.

The dataset is given as:

  • x: 8  15  3  7  2  14
  • y: 15  21  6  12  3  20

Using a graphing calculator, we have the following parameters:

<h3>X Values </h3>
  • ∑x = 49
  • Mean = 8.167
  • ∑(X - Mx)2 = SSx = 146.833

<h3>Y Values </h3>
  • ∑y = 77
  • Mean = 12.833
  • ∑(Y - My)2 = SSy = 266.833

<h3>X and Y Combined </h3>
  • N = 6
  • ∑(X - Mx)(Y - My) = 194.167

The correlation coefficient (r) is then calculated as:

r = \frac{\sum{((x - My)(Y - Mx)) }}{ \sqrt{((SSx)(SSy))}}

This gives

r = \frac{194.167 }{ \sqrt{((146.833)(266.833))}}\\

r = 0.9809

Approximate

r = 0.981

Hence, the value of correlation coefficient (r) for the dataset is 0.981

Read more about correlation coefficient at:

brainly.com/question/4219149

3 0
2 years ago
Stephen evaluated (6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). His work is shown below
Maksim231197 [3]

Answer:

The step 4 and 5 describe the errors Stephen made.

Step-by-step explanation:

Given : Stephen evaluated (6.34\times 10^{-7})(4.5\times 10^3).  His work is shown below.

To find : Which two statements describe the errors Stephen made?

Solution :

Step 1 - (6.34\times 10^{-7})(4.5\times 10^3)

Step 2 - (6.34\times 4.5)(10^{-7}\times 10^3)

Step 3 - (28.53)(10^{-4})

Step 4 - 28.53\times 10^{4}

Error is the step as 4 sign is negative.

So correct step is 28.53\times 10^{-4}

Step 5 - 28.53\times 10^{3}

Error is the step as there is 4 in place of 3.

So correct step is 28.53\times 10^{-4}

The step 4 and 5 describe the errors Stephen made.

7 0
3 years ago
Read 2 more answers
help!!!! I'm going to be doing quick questions. you answer them, you get a brainly. Starting with this one!!!!!!!! I think it's
stepladder [879]

Answer:

the answer is C

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • The solution set of the equation is If √x + 3 = 3 -x is?
    5·1 answer
  • For the function f defined by f(x)=5x−12 find f(−x),−f(x), and −f(−x).
    15·1 answer
  • On his 8 tests, Hong earned a total of 568 points. What<br> mean number of points earned per test?
    11·2 answers
  • I appreciate all the help guys! Need help on this one y’all
    5·1 answer
  • A law firm has sixsix senior and sevenseven junior partners. A committee of three partners is selected at random to represent th
    13·2 answers
  • Which problem can we solve with 1/4 ÷ 3
    7·1 answer
  • −2 1/2 ÷ 6 =?
    9·1 answer
  • Which of the following is supporting evidence of the given statement?
    14·1 answer
  • ANSWER FAST PLEASE
    11·1 answer
  • 5.000g rounded to the nearest whole gram
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!