Question

Assume that the GPA of a randomly chosen college student has a normal distribution with mean 2.84 and standard deviation 0.42.

a. Find the probability that a randomly chosen college student has a GPA of at least 2.30.

b. If then college students are independently selected, what is the probability that exactly nine of them have a GPA of at least 2.30.

Answer 1

Solution :

Given that ,

mean = = 2.84

standard deviation = = 0.42

P(X > 2.30) = 1 - P(x < 2.30)

= 1 - P((x - ) / < ( 2.30-2.84) / 0.42)

= 1 - P(z < -1.29)   Using standard normal table,

= 1 - 0.0985

= 0.9015

P(x > 2.30) = 0.9015

Probability = 0.9015

(b)

n=9

P( > 2.30) = 1 - P( <2.30 )

= 1 - P((x - ) / /n < ( 2.30-2.84) /0.42/9 )

= 1 - P(z <-3.86 )   Using standard normal table,

= 1 - 0.0001   

= 0.9999

P( > 2.30) = 0.9999

Probability = 0.9999