Question

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 29 points on this test, rounded to five decimal places?

(b) What is the 20 percentile of the distribution of test scores, rounded to three decimal places?

Answer 1

Solution :

Given ,

mean = = 22

standard deviation = = 2

P(x >29 ) = 1 - P(x<29 )

= 1 - P[(x -) / < (29 -22) / 2]

= 1 - P(z <3.5 )

Using z table

= 1 - 0.9998

= 0.00020

proportion= 0.00020

B)

Using standard normal table,

P(Z < z) =20 %

= P(Z < z) = 0.20  

= P(Z < -0.84) = 0.20

z = - 0.84 Using standard normal z table,

Using z-score formula  

x= z * +

x= -0.84 *2+22

x= 20.320