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Heights of adult males are approximately normally distributed with a mean of 66.6 inches and a...

Heights of adult males are approximately normally distributed with a mean of 66.6 inches and a standard deviation of 1.9 inches. If a sample of 50 adult males are​ chosen, what is the probability their mean height will be between 67 inches and 67.4 ​inches? Report your answer to four decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution :

= / n = 1.9 / 50 = 0.2687

= P[(67 - 66.6) / 0.2687 < ( - ) / < (67.4 - 66.6) / 0.2687)]

= P(1.49 < Z < 2.98)

= P(Z < 2.98) - P(Z < 1.49)

= 0.9986 - 0.9319

= 0.0667

Probability = 0.0667

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