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In: Statistics and Probability

The times that college students spend studying per week have a distribution that is skewed to...

The times that college students spend studying per week have a distribution that is skewed to the right with a mean of 7.0 hours and a standard deviation of 2.4 hours. Find the probability that the mean time spent studying per week for a random sample of 45 students would be

a. between 7.4 and 8.2 hours.

b. less than 7.4 hours

. Note 1: Round your z values to 2 decimal places before looking them up in the table or using them in a calculator. Note 2: Keep 4 decimal places in your final answers.

Solutions

Expert Solution

Solution :

Given that,

mean = = 7.0

standard deviation = = 2.4

n = 45

= 7.0

= / n = 2.4 45 = 0.3578

a ) P (7.4 < < 8.2 )

P ( 7.4 - 7.0 /0.3578) < ( -  / ) < 8.2 - 7.0 / 0.3578)

P (0.4 /0.3578 < z < 1.2 / 0.3578)

P (1.12 < z < 3.35)

P ( z < 3.35 ) - P ( z < 1.12 )

Using z table

= 0.9996 - 0.8686

= 0.1310

Probability = 0.1310

b ) P( < 7.4 )

P ( - / ) < ( 7.4 - 7.0 / 0.3578 )

P ( z < 0.4 / 0.3578 )

P ( z < 1.12)

Using z table

= 0.8686

Probability = 0.8686

orchestra answered 2 years ago
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