Question

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.9 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 9.3 ounces. Round your answer to 4 decimal places.

(b) If 7 potatoes are randomly selected, find the probability that the mean weight is more than 8.5 ounces. Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 7.9

standard deviation = = 1.3

(a)

n = 4

= 7.9 and

= / n = 1.3 / 4 = 1.3 / 2 = 0.65

P( < 9.3) = P(( - ) / < (9.3 - 7.9) / 0.65) = P(z < 2.1538)

Using standard normal table,

P( < 9.3) = 0.9844

Probability = 0.9844

(b)

n = 7

= 7.9 and

= / n = 1.3 / 7

P( > 8.5) = 1 - (P( < 8.5) = 1 - P(( - ) / < (8.5 - 7.9) / 1.3/7 = 1 - P(z < 1.2211)

Using standard normal table,

P( < 9.3) = 1 - 0.8890 = 0.1110

Probability = 0.1110