Question

In: Statistics and Probability

15. A population has a mean of 64.7 and a standard deviation of 11.9. Assuming ,...

15. A population has a mean of 64.7 and a standard deviation of 11.9. Assuming , the probability, rounded to four decimal places, that the sample mean of a sample of size 32 elements selected from this populations will be between 62.5 and 67.1 is:

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 64.7

standard deviation = = 11.9

n = 32

= 64.7

=  / n= 11.9/ 32=2.104

P(62.5<     < 67.1) = P[(62.5-64.7) / 2.104< ( - ) /   < (67.1-64.7) / )2.104]

= P( -1.05< Z < 1.14)

= P(Z <1.14) - P(Z < -1.05)

Using z table

=0.8729 - 0.1469

probability= 0.7260


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