A random sample of size n = 72 is taken from a population with mean mu = -13.7 a

Question

A random sample of size n = 72 is taken from a population with mean mu = -13.7 and standard deviation sigma = 9. Use Table 1. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard deviation" to 4 decimal places.) b. What is the probability that the sample mean is less than -14? Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. What is the probability that the sample mean falls between -14 and -13? (Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Explanation / Answer

Answer to the questions:

n=72
Mean = -13.7
Stdev = 9

a.

E(X) = Mean = -13.7
Std error = 9/sqrt(72) = 1.061

b.

P(X<-14)
=P(Z< -14-(-13.7)/1.061)
= P(Z<-.283)
=.39

c.

P(-14<X<-13)
=P(-.283<Z<.66)
=.7454-.3897
=.36

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