Question 1120530: Max Scherzer, the starting pitcher for the Nationals, on average, has a 0.250 probability of hitting the ball in a single "at bat". In one game, he gets 6 "at bats."
(a) Let X be the number of hits that Max gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
(b) Find the probability that he gets at least 4 hits in the one game. (Round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.
11. Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles per gallon and a standard deviation of 10 miles per gallon. Show all work. Just the answer, without supporting work, will receive no credit.
(a) What is the probability that a randomly selected car gets between 20 and 25 miles per gallon? (Round the answer to 4 decimal places)
(b) Find the 80th percentile of the miles per gallon distribution. (Round the answer to 2 decimal places)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! a. 6 trials or n. p=0.250 q=0.750
b. 4 hits is 6C4 or 15 ways that can happen*0.25^4*0.75^2,=0.0330.
5 hits is 6*0.25^5*0.75 or 0.0044
6 hits is 0.25^6 or 0.0002
At least 4 hits is that sum or 0.0376 or round to 0.038
Want the z score for this where z=(x-mean)/sd
z is between (20-23.5)/10 or -0.35 and +0.15
That probability is 0.1964
z(0.80)=+0.842
0.842=(x-mean)/sd
8.42=x-mean
x=31.92 mpg
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