Question

The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.6 ounce. ​

(a) What is the probability that a randomly selected carton has a weight greater than 10.33 ​ounces? ​

(b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 10.33 ​ounces?

Answer 1

Solution :

Given that,

mean = = 10

standard deviation = = 0.6

a ) P (x > 10.33 )

= 1 - P (x < 10.33)

= 1 - P ( x -  / ) < ( 10.33 - 10 / 0.6)

= 1 - P ( z < 0.33 / 0.6 )

= 1 - P ( z < 0.55)

Using z table

= 1 - 0.7088

= 0.2912

Probability = 0.2912

b ) n = 16

= 1200

₌ / n = 0.6 16 =0.15

P ( > 10.33 )

= 1 - P ( < 10.33)

= 1 - P (  - /) < ( 10.33 - 10 / 0.15)

= 1 - P ( z < 0.33 / 0.15 )

= 1 - P ( z < 2.2 )

Using z table

= 1 -0.9861

=0.0139

Probability = 0.0139