Question

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.2 ounces and a standard deviation of 1.3 ounces.

(a) If 4 potatoes are randomly selected, find the probability that the mean weight is less than 10.0 ounces. Round your answer to 4 decimal places.

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.6 ounces. Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 8.2

standard deviation = = 1.3

a) n = 4

= 8.2 and

= / n = 1.3 / 4 = 0.65

P( < 10.0) = P(( - ) / < (10.0 - 8.2) / 0.65)

= P(z < 2.7692)

Using standard normal table,

=0.9972

Probability = 0.9972

b) n = 6

= 8.2 and

= / n = 1.3 / 6 = 0.5307

P( > 9.6) = 1 - P( < 9.6)

= 1 - P(( - ) / < (9.6 - 8.2) / 0.5307)

= 1 - P(z < 2.6380)

Using standard normal table,

= 1 - 0.9958

= 0.0042

Probability = 0.0042