Question

If possible could you show me how to do this in excel?

Weights of a population have a mean (µ) of 180 pounds and standard deviation (σ) of 15 pounds.

If random samples of size n = 5 are selected from this population, what percentage of the sample means would you expect to be (or “What is the probability that any sample mean (x-bar) is”)

1. (6 points)Between 179 and 181 pounds?

2. (6 points)Less than 177 pounds?

Answer 1

This is a normal distribution question with

Sample size (n) = 5

Since we know that

a) x1 = 179

x2 = 181

P(179.0 < x < 181.0)=?

This implies that

P(179.0 < x < 181.0) = P(-0.1491 < z < 0.1491) = P(Z < 0.1491) - P(Z < -0.1491)

P(179.0 < x < 181.0) = 0.5592626370546617 - 0.4407373629453383

b) x = 177

P(x < 177.0)=?

The z-score at x = 177.0 is,

z = -0.4472

This implies that

PS: you have to refer z score table to find the final probabilities.

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