2. A university administrator expects that 30% of students in a core course will receive an A. He looks at the grades assigned to 100 students. The probability that the proportion of students that receive an A is 0.25 or less is .

The probability that the proportion of students that receive an A is 0.25 or less is = 0.1379

Step-by-step explanation:

Given -

A university administrator expects that 30% of students in a core course will receive an A.

Sampling distribution of sample proportion = p  = 30% = 0.30

Sample size ( n ) = 100

Standard deviation of sample proportion  = = = .0458

The probability that the proportion of students that receive an A is 0.25 or less is =  

           =        Putting

           =       Using Z table

          = 0.1379

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.