Question

If a population distribution has a mean of 70 and a standard deviation of 17, what is the percentile for a sample mean of 75 with a sample size of 70? Report your answer to the fourth decimal place and in proportion form (not in percentages).

Answer 1

Solution:

Given that,

mean = = 70

standard deviation = = 17

Sample size = n = 70

So,

   = 70

=  ( /n) = (17 / 70 ) = 2.0319

p (   < 75 )

= p ( - /) < (75 - 70 / 2.0319)

= p ( z < 5 / 2.0319)

= p ( z < 2.46 )

Using z table

= 0.9931

Proportion = 0.9931