Question

In: Statistics and Probability

4]The GPAs of all students enrolled at a large university have an approximately normal distribution with...

4]The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Find the probability that the mean GPA of a random sample of 20 students selected from this university is 2.93 to 3.11

Expert Solution

Solution :

Given that ,

mean = = 3.02

standard deviation = = 0.29

n = 20

= 3.02

= / $\sqrt$ n= 0.29 / $\sqrt$ 20=0.065

P(2.93< < 3.11) = P[(2.93-3.02) / 0.065< ( - ) / < (3.11-3.02) /0.065 )]

= P(-1.38 < Z <1.38 )

= P(Z < 1.38) - P(Z -1.38 )

Using z table

=0.9162-0.0838

=0.8324

probability=

orchestra answered 2 years ago

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