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A random variable X follows a normal distribution with mean 135 and standard deviation 12. If...

A random variable X follows a normal distribution with mean 135 and standard deviation 12. If a sample of size 10 is taken, find P (x̅ < 137). (4 decimal places) Find the answer using StatCrunch.

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Answer #1

Solution :

Given that ,

mean = = 135

standard deviation = = 12

n = 10

= = 135 and

= / n = 12 / 10 = 3.7947

P( < 137) = P(( - ) / < (137 - 135) / 3.7947)

= P(z < 0.527)

= 0.7009

Probability = 0.7009

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