Question

A set of final exam grades in ST2500 course is normally distributed with mean 70 and standard deviation of 8. (a) What is the probability of getting a grade of A(greater or equal 80) on this exam? (4) (b) What is the probability of that a student scored between 65 and 79? (4) (c) The probability is 10% that a student taking the exam scores higher than what grade?

Answer 1

Solution :

Given that ,

mean = = 70

standard deviation = = 8

a) P(x > 80 ) = 1 - p( x< 80 )

=1- p P[(x - ) / < (80 - 70) / 8]

=1- P(z < 1.25 )

Using z table,

= 1 - 0.8944

= 0.1056

b) P( 65< x < 79 ) = P[(65 - 70)/ 8) < (x - ) /  < (79 - 70) / 8) ]

= P(- 0.63< z < 1.13)

= P(z < 1.13 ) - P(z < - 0.63 )

Using z table,

= 0.8708 - 0.2643

= 0.6065

c) Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0. 10

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.9

= P(Z < 1.28 ) = 0. 9

z = 1.28

Using z-score formula,

x = z * +

x =1.28 * 8 + 70

x = 80.24