STAT 16 TEST 3

  1. 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
    1. at least 6 days of rain
    2. no rain
    3. at most 4 days of rain

 

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

 

  1. 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:
    1. At least 158 lbs.
    2. Between 130 lbs. And 163 lbs.

 

  1. 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?

 

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

 

  1. 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.

 

  1. 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.

 


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