# A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 25.?

A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 25. Compute the probability the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)

(a) Greater than 59.

(b) Less than 54.

(c) Between 54 and 59.

### 1 Answer

Relevance

- Mike GLv 75 months ago
μ = 55

σ = 14

n = 25

x̅ = sample mean

a) z(x̅=59) = (59-55)/(14/√25)

= 1.4286

From the z-tables

P(z>1.4286) =

0.0764

b) z(x̅=54) = (54-55)/(14/√25)

= -0.3571

P(z<-0.3571) =

0.3594

c) P(-0.3571<z<1.4286) =

0.5642

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