Question

A manufacturer knows that their items have a normally
distributed length, with a mean of 12.4 inches, and standard
deviation of 2.1 inches.

If 21 items are chosen at random, what is the probability that
their mean length is less than 11.2 inches?

P(¯x<11.2)=P(x¯<11.2)=

Answer #1

Solution :

Given that ,

mean = = 12.4

standard deviation = = 2.1

= / n = 2.1 / 21 = 0.4583

P( < 11.2) = P(( - ) / < (11.2 - 12.4) / 0.4583)

= P(z < -2.6184)

= 0.0044

P(
< 11.2) = **0.0044**

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