Question

Asked Aug 7, 2019

215 views

Number 15 A B C D

Step 1

**Note:**

Thank you for the question. However, your question has more than 3 parts. We are solving first three parts.

Step 2

Denote *X* as the observation. It is given that mean *μ* = 80 and standard deviation *σ* = 14.

**Part a:**

If a random sample of size *n *is taken from a population having mean µ and standard deviation σ then, as the sample size increases (*n *≥ 30), the sample mean *X*-bar approaches the normal distribution with mean µ and standard deviation σ/sqrt (n).

The sampling distribution of x-bar has the mean value of 80 with the standard deviation of 14/sqrt (49). That is, X follows normal distribution with mean value of 80 and standard deviation of 2.

** **

Step 3

**Part b:**

P(x-bar > 83):

The probability of x-bar greater than 83 is,

P(x-bar > 83) = 1- P(x-bar < 83)

Note: P(x-bar < 83) = 0. 933 [ EXCEL f...

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