In: Statistics and Probability
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:
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