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Assume that the heights of 30,000 male students at a university are normally distributed with a...

Assume that the heights of 30,000 male students at a university are normally distributed with a mean of 68.0 inches and a standard deviation of 3.0 inches. A random sample of 35 students is taken and the mean is calculated. What is the probability that this mean value will be between 66.8 inches and 68.8 inches?

Math   Statistics-And-Probability   
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Answer #1

Solution :

= / n = 3 / 35

= P[(66.8 - 68) / 3 / 35 < ( - ) / < (68.8 - 68) / 3 / 35)]

= P(-2.37 < Z < 1.58)

= P(Z < 1.58) - P(Z < -2.37)

= 0.9429 - 0.0089

= 0.9340

Probability = 0.9340

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