Dis... Check Your work 40.00 points Suppose that we will randomly select a sampl

Question

Dis... Check Your work 40.00 points Suppose that we will randomly select a sample of 64 measurements from a population having a 20 and a standard deviation equal to 4. mean equal to (a) Describe the shape of the sampling distribution of the sample mean Do we need to make any assumptions about the shape population? non of the Why or why Normaly distributed B: no E, because the sample size is (b) Find the mean and the standard deviation of the sampling distributon of the sample mean (Round your answer to 1 decimal place.) (c) Calculate the probability that we wil obtain a sample mean greater than 21:that is, calculate PGE 21). Hint: Find the z value corresponding to 21 by using ur and a because we to calculate a probability about i. (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Ro z-scores to 2 decimal places.) PR 21) (d) Calculate the probabilty that we will obtain a sample mean less than 1 that is, calculate PGE 19.385) (use the rounded standard error to compute the rounded z-core used to find the probability. Round your answer to 4 decimal places. 19.385) PR Hints References eBook & Resources Hint #1 Check my work

Explanation / Answer

b)
mean = 20
standard deviation = 4

n = 64

c)
P(X >21)

z = ( x - mean) / (s/sqrt(n))
= ( 21 - 20) / (4/sqrt(64))
= 2
P(X > 21) = P( z > 2) = 0.0228

d)
P(X < 19.385)

z =( x - mean) / (s/sqrt(n))
= (19.385 - 20) / (4/sqrt(64))
= -1.23
P(X <19.385) = P( z < -1.23) = 0.1093

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