**STAT
16 TEST 3**

- From past experience, a weather forecaster has determined that 80% of time it does not rain. Find the probability that for the next two weeks

- at least 6 days of rain
- no rain
- at most 4 days of rain

- Suppose X is normally distributed with mean = 1000 and SD = 50. Find prob.:
- if P( X > c ) = .3274, find c
- if P( Z > -0.66 )
- P( 920 < X < 1120 )

- The breaking strength of cables manufactured by a certain company has a normal distribution with a mean strength of 140 pounds and standard deviation of 14. Find the probability that a randomly picked cable will have breaking strength:
- At least 158 lbs.
- Between 130 lbs. And 163 lbs.

- The probability that an
electric sander will last between 500 and 600 hours before it needs repairs
is .78.� In a school district, 100
sanders are in use in different woodworking classes. What is the
approximate probability that
**more than**73 sanders will last between 500 and 600 hours?

- Given the population { 17, 9, 7, 1, 5, 3,}
- Find population mean and var.
- Find the mean and var. of the sampling distribution of n=2 ( without replacement )
- Show that the formulas on page 315,6 hold

- The time Joe takes to change the oil in any car has a certain probability distribution with a mean of 10 minutes per car with a standard deviation of 3 minutes.� If he has to change the oil in 245 cars, find the approximate probability that it will take him more then 10.3 minutes per car.

- A tire manufacturer knows that their current tire release is normal with a with an average tread life of 60000 miles and standard deviation of 7000 miles.� If this manufacturer wants to have at most 5% of the returned before failure what should the guarantee be in miles.