Question

Luciana's laptop has 3,000 pictures. The size of the pictures is skewed to the right, with a mean of 3.7MB and a standard deviation of 0.78MB.

Part A: Can you accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS of 20 pictures? Explain. (4 points)

Part B: If you take a random sample of 60 pictures instead of 20, explain how the Central Limit Theorem allows you to find the probability that the mean picture size is more than 3.8MB. Calculate this probability and show your work. (6 points)

Answer 1

Solution :

Given that ,

mean = = 3.7

standard deviation = = 0.78

A.

P(x > 3.8) = 1 - P(x < 3.8)

= 1 - P[(x - ) / < (3.8 - 3.7) / 0.78)

= 1 - P(z < 0.1282)

= 1 - 0.551

= 0.449

Probability = 0.449

B.

= / n = 0.78 / 60 = 0.1007

P( > 3.8) = 1 - P( < 3.8)

= 1 - P[( - ) / < (3.8 - 3.7) / 0.1007]

= 1 - P(z < 0.9930)

= 1 - 0.8396

= 0.1604

Probability = 0.1604