Question

Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.2 ounces and a standard deviation of 1.2 ounces.

(a) If 4 potatoes are randomly selected, find the probability that the mean weight is less than 9.5 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 9.5 ounces. Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 8.2

standard deviation = = 1.2

(a)

= / n = 1.2 / 4 = 0.6

P( < 9.5) = P(( - ) / < (9.5 - 8.2) / 0.6)

= P(z < 2.1667)

= 0.9849

Probability = 0.9849

(b)

= / n = 1.2 / 6 = 0.4899

P( > 9.5) = 1 - P( < 9.5)

= 1 - P[( - ) / < (9.5 - 8.2) / 0.4899]

= 1 - P(z < 2.6536)

= 1 - 0.996

= 0.004

Probability = 0.004