A manufacturer knows that their items have a normally distributed length, with a mean of 8.1...

A manufacturer knows that their items have a normally distributed length, with a mean of 8.1 inches, and standard deviation of 2.4 inches. If 11 items are chosen at random, what is the probability that their mean length is less than 9.3 inches? (Give answer to 4 decimal places.)

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Expert Solution

Solution :

Given that ,

mean = = 8.1

standard deviation = = 2.4

= / n = 2.4 / 11 = 0.7236

P( < 9.3) = P(( - ) / < (9.3 - 8.1) / 0.7236)

P(z < 1.6584)

= 0.9514

Probability = 0.9514

orchestra answered 1 year ago

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