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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 50 exams has a sample mean between 74 and 75?

a. 0.3810

b. 0.1210

c. 0.4641

d. 0.3790

e. 0.1190

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 75

standard deviation = =   6

n = 50

= 75

=  / n= 6 / 50=0.849

P(74<     < 75) = P[(74-75) / 0.849< ( - ) /   < (75-75) /0.849 )]

= P( -1.18< Z <0 )

= P(Z <0) - P(Z < -1.18)

Using z table

=0.5 -0.1190

PROBABILITY =0.3810

orchestra answered 2 years ago
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