Question

1- Suppose scores on an test are normally distributed. If the test has a mean of 100 and a standard deviation of 10, what is the probability that a person who takes the test will score 120 or more

2- The average amount of weight gained by a person over the winter months is uniformly distributed from 0 to 30 lbs. Find the probability a person will gain between 10 and 15 lbs during the winter months.

Answer 1

Solution :

Given ,

mean = = 100

standard deviation = = 10

P(x >120 ) = 1 - P(x<120 )

= 1 - P[(x -) / < (120-100) / 10]

= 1 - P(z < 2)

Using z table

= 1 - 0.9772

= 0.0228

probability= 0.0228

2.

Solution :

Given that,

a = 0

b = 30

P(c < x < d) = (d - c) / (b - a)

P(10 < x < 15) = (15 - 10) / (30 - 0) = 0.17

Probability = 0.17