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An unknown distribution has a mean of 90 and a standard deviation of 15. Samples of...

An unknown distribution has a mean of 90 and a standard deviation of 15. Samples of size n=25 are drawn randomly form the population. Find the probability that the sample mean is between 85 and 92 is the area under which curve?

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = 90

standard deviation = = 15

= / n = 15 / 25 = 3

= P[(85 - 90) /3 < ( - ) / < (92 - 90) / 3)]

= P(-1.67 < Z < 0.67)

= P(Z < 0.67) - P(Z < -1.67)

= 0.7586 - 0.0475

= 0.7111

Probability = 0.7111

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