Question

The heights of European 13-year-old boys can be approximated by a normal model with mean μ of 63.1 inches and standard deviation σ of 2.42 inches.

A) What is the probability that a randomly selected 13-year-old boy from Europe is taller than 65.1 inches?

(use 4 decimal places in your answer)

B) A random sample of 4 European 13-year-old boys is selected. What is the probability that the sample mean height x is greater than 65.1 inches?

(use 4 decimal places in your answer)

C) A random sample of 9 European 13-year-old boys is selected. What is the probability that the sample mean height x is greater than 65.1 inches?

(use 4 decimal places in your answer)

Answer 1

A) x = 65.1

P(x > 65.1)=?

The z-score at x = 65.1 is,

z = 0.8264

This implies that

B) Sample size (n) = 4 Since we know that

P(x > 65.1)=?

The z-score at x = 65.1 is,

z = 1.6529

This implies that

P(x > 65.1) = P(z > 1.6529) = 1 - 0.9508243914241373

C) Sample size (n) = 9 Since we know that P(x > 65.1)=?

The z-score at x = 65.1 is,

z = 2.4792

This implies that

PS: you have to refer z score table to find the final probabilities.

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