A random sample of size n = 62 is taken from a population with mean = 11.8 and s

Question

A random sample of size n = 62 is taken from a population with mean = 11.8 and standard deviation = 4. Use Table 1.

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.)

What is the probability that the sample mean is less than 12? Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that the sample mean falls between 12 and 11? (Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

A random sample of size n = 62 is taken from a population with mean = 11.8 and standard deviation = 4. Use Table 1.

Explanation / Answer

a.

Expected value = -11.8

Standard Error = 4/sqrt(62) = 0.5080

b.

z-score corresponding to -12 = (-12 - (-11.8))/0.5080 = - 0.3937

P(mean < -12) = P ( z < -0.3937 ) = 0.3469

c.

z-score corresponding to -11 = (-11 - (-11.8))/0.5080 = 1.5748

P( -12 < mean < -11 ) = P( -0.3937 < z < 1.5748 ) = P( z < 1.5748) - P(z < -0.3937 ) = 0.9423 - 0.3469 = 0.5954

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