Question

The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.5 ounce. ​(a) What is the probability that a randomly selected carton has a weight greater than 8.12 ​ounces? ​(b) A sample of 36 cartons is randomly selected. What is the probability that their mean weight is greater than 8.12 ​ounces? ​(a) The probability is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

a)

Given,

= 8 , = 0.5

We convert this to standard normal as

P( X < x) = P (Z < x - / )

So,

P( X > 8.12) = P( Z > 8.12 - 8 / 0.5)

= P( Z > 0.24)

= 0.4052

b)

Using central limit theorem,

P( < x) = P( Z < x - / / sqrt(n) )

So,

P( > 8.12 ) = P( Z > 8.12 - 8 / 0.5 / sqrt(36) )

= P( Z > 1.44)

= 0.0749