Question

In a normal distribution 31% of the items are under 45 and 8% of the items are over 64. find the mean and standard deviation of the distribution. given ϕ(0.5)  0.1915 and ϕ(1.4)  0.4192

Answer 1

In the attachment I have answered this problem.

I have explained this problem detailly
in 3 attachments.

I hope this answer help you

Answer 2

Mean = 49.95  & SD = 10

Step-by-step explanation:

z = -0.495  for 31% of the items are under 45

8% of the items are over 64

=> 92% are below 8  

=> z score = 1.405    of items over 64

z score = ( Value - Mean)/SD

=> -0.495 = (45 - Mean) SD

=> -0.495SD = 45 - Mean

=> Mean = 45 + 0.495SD

z score = ( Value - Mean)/SD

=>  1.405 = (64 - Mean) SD

=> 1.405SD = 64 - Mean

=> Mean = 64  - 1.405SD

45 + 0.495SD = 64  - 1.405SD

=> 1.9SD = 19

=> SD = 10

Mean = 64  - 1.405*10  = 49.95

Learn more:

Assume that adults have iq scores that are normally distributed with ...

https://brainly.in/question/11133397

Use technology or the z-distribution table on pages A-1 to A-2 in the ...

https://brainly.in/question/13301238

For normal distribution with mean as 500 and SD as 120,What is the ...

https://brainly.in/question/13287196