Question

The times that college students spend studying per week have a distribution skewed to the right with a mean of 8.3 hours and a standard deviation 2.6 of hours. Find the probability that the mean time spent studying per week for a random sample of 55 college students would be a. between 7.6 and 8.4 hours. Round your answer to two decimal places. b. less than 8.1 hours. Round your answer to two decimal places.

THE ANSWERS ARE NOT .49 AND .19

Answer 1

Solution :

Given that ,

mean = = 8.3

standard deviation = = 2.6

n = 55

= = 8.3

= / n = 2.6 / 55 = 0.3506

a)

P(7.6 < < 8.4) = P((7.6 - 8.3) / 0.3506<( - ) / < (8.4 - 8.3) / 0.3506))

= P(-2.00 < Z < 0.29)

= P(Z < 0.29) - P(Z < -2.00) Using standard normal table,  

= 0.6141 - 0.0228

= 0.5913

Probability = 0.59

b)

P( > 8.1) = 1 - P( < 8.1)

= 1 - P(( - ) / < (8.1 - 8.3) / 0.3506)

= 1 - P(z < -0.57)

= 1 - 0.2843 Using standard normal table.

= 0.7157

Probability = 0.72