Question

A manufacturer knows that their items have a normally distributed length, with a mean of 18 inches, and standard deviation of 4.2 inches.

If 20 items are chosen at random, what is the probability that their mean length is less than 15.5 inches? (Give answer to 4 decimal places.)

A manufacturer knows that their items have a normally distributed length, with a mean of 6.4 inches, and standard deviation of 1.2 inches.

If 10 items are chosen at random, what is the probability that their mean length is less than 5.4 inches? (Give answer to 4 decimal places.)

Answer 1

Solution :

1) Given that ,

= 18

= / n = 4.2/ 20 = 0.939

P( < 15.5 ) = P(( - ) / < (15.5 - 18) / 0.939)

= P(z < -2.66 )

Using z table

= 0.0039

2) Given that ,

= 6.4

= / n = 1.2/ 10 = 0.379

P( < 5.4 ) = P(( - ) / < (5.4 - 6.4) / 0.379)

= P(z < -2.64 )

Using z table

= 0.0041