Question

A manufacturer knows that their items have a normally
distributed length, with a mean of 17.4 inches, and standard
deviation of 2.4 inches.

If one item is chosen at random, what is the probability that
it is less than 15.7 inches long?

Answer #1

**Solution :**

Given that ,

= 17.4

= 2.4

A sample of size n = 1 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 17.4

SD = = 2.4/1 = 2.4

Find P( < 15.7 )

= P[( - )/ < (15.7 - 17.4)/2.4]

= P[Z < -0.708]

= 0.2395 ........ using z-table

**P(
< 15.7 ) = 0.2395**

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