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In: Statistics and Probability

The marks on a statistics midterm test are normally distributed with a mean of 75 and...

The marks on a statistics midterm test are normally distributed with a mean of 75 and a standard deviation of 6. What is the probability that a sample of 25 exams has a sample mean between 71 and 73?

a. 0.45293

b. 0.04793

c. 0.0475

d. 0.0485

e. 0.04707

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 75

standard deviation = = 6

n = 25

= 75

=  / n= 6 / 25=1.2

P(71<     < 73) = P[(71 - 75) /1.2 < ( - ) /   < (73 - 75) /1.2 )]

= P( -3.33< Z < -1.67)

= P(Z <-1.67 ) - P(Z < -3.33)

Using z table

=0.0475 - 0.0004

=0.0471

orchestra answered 2 years ago
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