Question

Given the population mean, μ = 45, and the population standard deviation, σ = 15 with a sample size of, n = 100.n = 100. Determine P ( x ¯ ≤ 42 ). To do this problem first determine the sampling mean and the sampling standard deviation in order to convert to a z-score. Round your answer to 4 decimals.

Answer 1

Solution :

Given that,

mean = = 45

standard deviation = =15

n = 100

= 45

=  / n = 15 / 100=1.5

P( < 42) = P[( - ) / < (42-45) /1.5 ]

= P(z < -2)

Using z table      

probability= 0.9772