In: Statistics and Probability
A researcher is working with a normally distributed population with a mean of 27 and standard deviation of 10. If you randomly choose a sample 169 participants, what proportion of the sample means will be less than 25? Show all of your calculations for full credit.
Solution :
Given that,
mean = = 27
standard deviation = = 10
n = 169
= 27
= / n = 10/ 169=0.769
P( <25 ) = P[( - ) / < (25-27) / 0.769]
= P(z <-2.60 )
Using z table
= 0.0047
probability= 0.0047