Question

In: Statistics and Probability

Let X have Normal distribution with mean 45 and variance 81. If a random sample of...

Let X have Normal distribution with mean 45 and variance 81. If a random sample of size 25 is taken, which of the following is the probability that the sample average is between 41.40 and 45.63?

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 45

varianc= 81 SO

standard deviation = = 9

n = 25

= 45

=  / n= 9/ 25=1.8

P(41.40<     <45.63 ) = P[(41.40 - 45) / 1.8< ( - ) /   < (45.63-45) /1.8 )]

= P(-2 < Z <0.35 )

= P(Z < 0.35) - P(Z <-2 )

Using z table

=0.6368-0.0228

=0.6140

probability= 0.6140


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