please answer all questions ans subs thank you 1. Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 5 miles per hour. Let X be the...

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1. Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.



a. What is the distribution of X? X ~ N(       ,        )


b. If one car is randomly chosen, find the probability that it is traveling more than 74 mph?


c. If one of the cars is randomly chosen, find the probability that it is traveling between 79 and 82 mph?


d. 83% of all cars travel at least how fast on the freeway?           mph.

2. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.7 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.



a. What is the distribution of X? X ~ N(        ,        )


b. What is the median recovery time?        days


c. What is the Z-score for a patient that took 5.7 days to recover?


d. What is the probability of spending more than 3.9 days in recovery?


e. What is the probability of spending between 5 and 6 days in recovery?


f. The 70th percentile for recovery times is?          days.

3. The number of seconds XX after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ U(         ,         )

then the sampling distribution is

2. Suppose that 40 classes are clocked.  What is the distribution of ¯x for this group of classes? ¯x ~ N(     ,     )


3. What is the probability that the average of 40 classes will end with the second hand between 23 and 31 seconds?