A random sample of size n Use Table 1 72 is taken from a population with mean -1

Question

A random sample of size n Use Table 1 72 is taken from a population with mean -13.7 and standard deviation -9 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 error to 4 decimal places.) Expected value Standard error b. What is the probability that the sample mean is less than -14? (Round "" value to 2 decimal places, and final answer to 4 decimal places.) Probability 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.) Probability References Worksheet Exercise 7-9 Algo Search the web and Windows

Explanation / Answer

a) Expected value = -13.7
Standard error, SE = SD/sqrt(n) = 9/sqrt(72) = 1.06066

b) Formula : Z = (X - mean)/SE

P(X_bar < -14) = P(Z < (-14 + 13.7)/1.06066) = P(Z < -0.28) = 0.3897

c) P(-14 < X_bar < -13) = P(X_bar < -13) - 0.3897 = P(Z < (-13 + 13.7)/1.06066) - 0.3897 = P(Z < 0.66) - 0.3897
= 0.7454 - 0.3897 = 0.3557

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