Question

A normal distribution has a standard deviation equal to 26. What is the mean of this normal distribution if the probability of scoring above

x = 183

is 0.0228? (Round your answer to one decimal place.)


You may need to use the appropriate table in Appendix C to answer this question.

https://www.webassign.net/priviterastats3/priviterastats3_appendix_c.pdf

Answer 1

Solution:-

Given that,

x = 183

standard deviation = = 26

Using standard normal table,

P(Z > z) = 0.0228

= 1 - P(Z < z) = 0.0228  

= P(Z < z) = 1 - 0.0228

= P(Z < z ) = 0.9772

= P(Z < 2.00 ) = 0.9772

z = 2.00

Using z-score formula,

x = z * +

183 = 2.00 * 26 +

= 183 - 52

= 131