Consider a normal population with ? = 36 and ? = 4.2. Calculate the z -score for

Question

Consider a normal population with ? = 36 and ? = 4.2. Calculate the z-score for an x of 44.3 from a sample of size 28. (Give your answer correct to two decimal places.)

Kindergarten children have heights that are approximately normally distributed about a mean of 39.5 inches and a standard deviation of 1.7 inches. If a random sample of 34 is taken, what is the probability that the sample of kindergarten children has a mean height of less than 39.5 inches? (Give your answer correct to four decimal places.)

Explanation / Answer

a) Z = (X - mean) / (sd/sqrt(n))

Z for 44.3 = (44.3 - 36) / (4.2 / sqrt(28)) = 10.46

b) Z for 39.5 = (39.5 - 39.5) / (1.7/sqrt(34)) = 0

P(sample mean less thn]an 39.5) = P(Z < 0) = 0.5

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