1. Suppose 15% of major league baseball players are left-handed. In a sample of
ID: 2957202 • Letter: 1
Question
1. Suppose 15% of major league baseball players are left-handed. In a sample of 12 major league baseball players, find the probability that :a) none are left handed
(b) at most six are left handed
(c) between 2 and 4, inclusive, are left handed
d) In a sample of 300 major league baseball players, about how many would you expect to be left handed? Why?
e) Find the variance of the x, the number of left-handed major league baseball players who are left-handed in a sample of 12 ball players.
2. A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly recorded the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. Find the following probabilities.
a) P( X = 10)
_______________
b) P( 4 < X < 9) =
_______________
c) P( X = 2)
_________________
d) P( X is at least 1)
___________________
e) P(X is no more than 3)
Problem 2 continued:
f) Find the mean of the probability distribution
_______________
g. Find the expected value of x, the number of cars speeding
_________________
h) Find the standard deviation of x, the number of cars speeding out of ten cars.
____________________
3. Which of the following can be classified as a binomial experiment?
a) shooting free throws until you make ten if your probability of making a given free throw is 0.60.
___________
b) Drawing four cards from a standard deck of cards without replacement and determining x, the number of aces drawn.
_____________
c) The probability of a defective light bulb being produced by a manufacturer of light bulbs is 0.03. If 12 light bulbs are selected from the entire production of light bulbs, let x represent the number of defective bulbs selected .
_____________
d) In a sample of 20 bolts, 3 are defective. Three bolts are selected at random without replacement and the number of defective bolts is recorded.
4. Construct the probability distribution of X, the number of boys in a 5 child family. Use a calculator or computer to set up lists and calculate the mean and variance of this probability distribution.
Explanation / Answer
Cramster rules say one problem per post. I'll answer the first one for you, but you'll need to repost the other three questions separately.
1. (a) (0.85)12 = 0.142
1. (b) binomcdf(12,0.15,6) = 0.999
1. (c) binomcdf(12,0.15,4)-binomcdf(12,0.15,1) = 0.976 - 0.443 = 0.533
1. (d) = np = 300(0.15) = 45
1. (e) 2 = npq = 300(0.15)(0.85) = 38.25
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.