Question

Lets say scores on an emotional intelligence test are normally distributed with a mean equal to 110.7 and a standard deviation equal to 24.5. The question asks: Above which value fall 50 percent of scores. PLEASE SHOW STEP BY STEP !!!

Answer 1

The percentage of fall 50 percent of scores is 0.68

Explanation:

Explanation:-

Given mean of the population = 110.7

standard deviation of the Population = 24.5

Let 'X' be the random variable in normal distribution

Given X = 50

Now

`Z = (x-mean)/(S.D)`

`Z = (50 - 110.7)/(24.5) = -2.477`

The probability that fall 50 percent of scores.

P( X < 50) = P( Z < -2.477)

= 1- P(Z>2.477)

= 1 - (0.5 + A(2.477)

= 0.5 - A(2.477)

= 0.5 - 0.4932

= 0.0068

The percentage of fall 50 percent of scores is 0.68