Question

The mean GPA of all college students is 2.95 with a standard deviation of 1.25.

What is the probability that a single MUW student has a GPA greater than​ 3.0? (Round to four decimal​ places)

What is the probability that 50 MUW students have a mean GPA greater than​ 3.0? (Round to four decial​ palces)

Answer 1

Solution :

Given ,

mean = = 2.95

standard deviation = = 1.25

P(x > 3) = 1 - P(x<3 )

= 1 - P[(x -) / < (3-2.95) / 1.25]

= 1 - P(z < 0.04)

Using z table

= 1 - 0.5160

= 0.4840

probability= 0.4840

b.

n = 50

=    = 2.95

= / n = 1.25 / 50 = 0.18

P( >3 ) = 1 - P( < 3)

= 1 - P[( - ) / < (3-2.95) /0.18 ]

= 1 - P(z <0.28 )

Using z table

= 1 - 0.6103

= 0.3897

probability= 0.3897