A random sample of size n = 80 is taken from a population with mean = 15.2 and s

Question

A random sample of size n = 80 is taken from a population with mean = 15.2 and standard deviation = 5. 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 error" to 4 decimal places.)
  Expected value _______
     Standard error   ________

b. What is the probability that the sample mean is less than 15? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)
Probability ____________

c. What is the probability that the sample mean falls between 15 and 14? (Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.)     
Probability _____________

Explanation / Answer

A) Expected value = -15.2

Standard error = SD/sqrt(n) = 5/sqrt(80) = 0.559

B) P(X < -15) = P((x - mean)/(SD/sqrt(n) < (-15 +15.2)/(5/sqrt(80))

= P(Z < 0.36)

= 0.6406

C) P(-15 < X < -14) = ((-15 + 15.2)/(5/sqrt(80)) < (X - mean)/(SD/sqrt(n) < (-14 + 15.2)/(5/sqrt(80))

= P(0.36 < Z < 2.15)

= P(Z < 2.15) - P(Z < 0.36)

= 0.9842 - 0.6406 = 0.3436

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