Question

GPA of the students who are taking Stat 50 class at bcc follows a normal distribution with a mean of 2.87 and a standard deviation of 0.43. If 35 students who are taking Stat 50 are selected, what is the probability that their average GPA is more than 2.97?

A) Not enough information is given to find the answer

B) Almost 0

C) 0.084

D) 0.408

2) GPA of the students who are taking Stat 50 class at bcc follows a normal distribution with a mean of 2.87 and a standard deviation of 0.43. If one student who is taking Stat 50 are selected, what is the probability that his or her average GPA is more than 2.97?

A) Not enough information is given to find the answer

B) 0.408

C) Almost 0

D) 0.084

Answer 1

Solution :

Given that,

mean = = 2.87

standard deviation = = 0.43

n = 35

1) = = 2.87

= / n = 0.43 / 35 = 0.0727

P( > 2.97) = 1 - P( < 2.97 )

= 1 - P[( - ) / < (2.97 - 2.87) / 0.0727 ]

= 1 - P(z < 1.376)

Using z table,    

= 1 - 0.916

= 0.084

correct option is = C

2) P(x > 2.97) = 1 - p( x< 2.97)

=1- p P[(x - ) / < (2.97 - 2.87) / 0.43 ]

=1- P(z < 0.233)

Using z table,

= 1 - 0.592

= 0.408

correct option is = B