Question

The weights of ice cream cartons are normally distributed with a mean weight of 13 ounces and a standard deviation of 0.6 ounce. ​(a) What is the probability that a randomly selected carton has a weight greater than 13.19 ​ounces? ​(b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 13.19 ​ounces?

Answer 1

Solution :

Given that ,

mean = = 13

standard deviation = = 0.6

(a)

P(x > 13.19) = 1 - P(x < 13.19)

= 1 - P[(x - ) / < (13.19 - 13) / 0.6]

= 1 - P(z < 0.32)

= 1 - 0.6255

= 0.3745

Probability = 0.3745

(b)

= / n = 0.6 / 25 = 0.12

P( > 13.19) = 1 - P( < 13.19)

= 1 - P[( - ) / < (13.19 - 13) / 0.12]

= 1 - P(z < 1.58)

= 1 - 0.9429

= 0.0571

Probability = 0.0571