Question

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 10.6 inches, and standard deviation of 3.3 inches.

If 46 items are chosen at random, what is the probability that their mean length is greater than 11.2 inches?

(Round answer to four decimal places)

Answer 1

Solution :

Given that,

mean = = 10.6

standard deviation = = 3.3

n=46

= =10.6

= / n = 3.3 / 46 = 0.487

P( > 11.2) = 1 - P( < 11.2)

= 1 - P[( - ) / < (11.2-10.6) /0.487 ]

= 1 - P(z <1.23 )

Using z table

= 1 - 0.8907

probability= 0.1093