Consider a normal population with ? = 39 and ? = 5.6. Calculate the z-score for

Question

Consider a normal population with ? = 39 and ? = 5.6. Calculate the z-score for an x of 47.1 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 39.9 inches and a standard deviation of 2.8 inches. If a random sample of 25 is taken, what is the probability that the sample of kindergarten children has a mean height of less than 39.6 inches? (Give your answer correct to four decimal places.) You may need to use the appropriate table in Appendix B to answer this question.

Explanation / Answer

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

= (47.1 - 39) / (5.6 / sqrt(28))

= 7.65

B) Z score 39.6 = (39.6 - 39.9) / (2.8 / sqrt(25))

= - 0.54

P(sample mean less than 39.6) = P(Z < - 0.54) = 0.2946

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