Question

1. Score (X) on a 100-point test is normally distributed with mean 89 and standard deviation 10.                                                         

What is the following probability:

P(85 < X < 95)

2. You took a sample of 25 students from the population in I.

What is the following probability:               

P(85 < Xbar < 95)

Answer 1

Solution :

Given that ,

mean = = 89

standard deviation = = 10

1) P(85 < x < 95) = P[(85 - 89)/ 10) < (x - ) /  < (95 - 89) /10 ) ]

= P(-0.40 < z < 0.60)

= P(z < 0.60) - P(z < -0.40)

Using z table,

= 0.7257 - 0.3446

= 0.3811

2) n = 25

= = 89

= / n = 10 / 25 = 2

P(85 < < 95)  

= P[(85 - 89) / 2 < ( - ) / < (95 - 89) / 2 )]

= P(-2.00 < Z < 3.00)

= P(Z < 3.00) - P(Z < -2.00)

Using z table,  

= 0.9987 - 0.0228   

= 0.9759