Mathematics, 21.02.2020 17:29 ptrlvn01

Historically, the average score of PGA golfers for one round is 73.9 with a standard deviation of 1.1. A random sample of 99 golfers is taken. What is the probability that the sample mean is between 73.9 and 74.03

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Answer from: valeriemccarty6212

38.10% probability that the sample mean is between 73.9 and 74.03.

Step-by-step explanation:

To solve this question, it is important 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 73.9, \sigma = 1.1, n = 99, s = \frac{1.1}{\sqrt{99}} = 0.1105$

What is the probability that the sample mean is between 73.9 and 74.03

This is the pvalue of Z when X = 74.03 subtracted by the pvalue of Z when X = 73.9. So

X = 74.03

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

By the Central Limit Theorem

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

$Z = \frac{74.03 - 73.9}{0.1105}$

Z = 1.18

Z = 1.18 has a pvalue of 0.8810.

X = 73.9

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

$Z = \frac{73.9 - 73.9}{0.1105}$

Z = 0

Z = 0 has a pvalue of 0.5

0.8810 - 0.5 = 0.3810

38.10% probability that the sample mean is between 73.9 and 74.03.

Answer from: Quest

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

Answer from: Quest

$given : \frac{3}{9} = \frac{x}{5}$

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x

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Historically, the average score of PGA golfers for one round is 73.9 with a standard deviation of 1....