Question

The average number of graduates for a school district has been 250 per year with a standard deviation of 30. What is the probability that the number of graduates next year will be:

a. Less than 220

b. Less than 325

c. Less than 285

d. More than 238

e. More than 300

f. More than 325

Answer 1

Solution :

Given that ,

mean = = 250

standard deviation = = 30

a.

P(x < 220) = P[(x - ) / < (220 - 250) / 30]

= P(z < -1)

= 0.1587

Probability = 0.1587

b.

P(x < 325) = P[(x - ) / < (325 - 250) / 30]

= P(z < 2.5)

= 0.9938

Probability = 0.9938

c.

P(x < 285) = P[(x - ) / < (285 - 250) / 30]

= P(z < 1.17)

= 0.879

Probability = 0.879

d.

P(x > 238) = 1 - P(x < 238)

= 1 - P[(x - ) / < (238 - 250) / 30)

= 1 - P(z < -0.4)

= 1 - 0.3446

= 0.6554

Probability = 0.6554

e.

P(x > 300) = 1 - P(x < 300)

= 1 - P[(x - ) / < (300 - 250) / 30)

= 1 - P(z < 1.67)

= 1 - 0.9525

= 0.0475

Probability = 0.0475

f.

P(x > 325) = 1 - P(x < 325)

= 1 - P[(x - ) / < (325 - 250) / 30)

= 1 - P(z < 2.5)

= 1 - 0.9938

= 0.0062

Probability = 0.0062