Geom/Binom Dist.
Suppose X has a binomial distribution with n = 500 and p = .3. Find the mean and standard deviation of the distribution.
Mean =150 Standard Deviation = 10.25
The probability that a 3 year old battery works is .7 and a graphing calculator requires 4 batteries to work. Mr. Woyna finds 4 batteries that are 3 years old in the math office. What is the probability that he puts them in a calculator and it works?
.74 = binompdf(4, .7, 4) = .2401
Abe takes random guesses on a multiple-choice test in Pre Calc. Each question has options a, b, c, and d. What is the average number of questions he has to answer before he gets one correct?
4
Trevor and Connor are going to compete in the 100-meter dash against each other. Based on previous results, they know that Trevor averages 11.5 seconds with a deviation of 1 second and Connor averages 10.5 seconds with a deviation of 0.5 seconds. On average, how much will Connor win by?
1 second
Give all 4 conditions for binomial random variables.
BINS (Binary, Independent, "n", success rate)
The probability that a telemarketing employee reaches a person is .11. Suppose they call 20 people in a night. What is the probability that they reach 3 or less people?
binomcdf(20, .11, 3) = .829
On Abe's multiple-choice test (4 choices per question), what is the probability that the first time he gets one right is on the 4th question?
geompdf(.25, 4) = .105
Over Meg's career, she hits the ball in a normal distribution with a mean of 200 feet and a standard deviation of 30 feet. Find the probability that a random hit will go more than 250 feet.
normalcdf(250, 10000, 200, 30) = .0478
Give all conditions needed for a geometric distribution.
Binary, Independent, "until", Success Rate
The probability that a telemarketing employee reaches a live person is .11. Suppose they call 20 people in a night. What is the probability that they reach less than 5 people?
binomcdf(20, .11, 4) = .939
Caitlyn tends to score once out of every 3 shots she takes on goal. What is the probability that she will score within the first 5 shots of the game?
geometcdf(1/3,5) = .8683
Trevor and Connor are going to compete in the 100-meter dash against each other. Based on previous results, they know that Trevor averages 11.5 seconds with a deviation of 1 second and Connor averages 10.5 seconds with a deviation of 0.5 seconds. What is their combined standard deviation?
1.12 seconds
(n C 5) p5 (.71)8 What is mean of the distribution?
n = 13 p = .29 Mean = 3.77
It is estimated that 10% of drivers turn on their blinker before changing lanes. In a random sample of 4 drivers, what is the probability that at least one person uses his or her blinker when changing lanes?
1 - binom(4, .1, 0) = .3439
Ethan has a history of making his free throws 45% of the time. What is the probability that he will make his first free throw before his 5th try in a game?
geometcdf(.45, 4) = .908
Mr. Woyna plans on racing (beating) Meg in the Lisle 5K. If Mr. Woyna averages 23 minutes with a standard deviation of 3 minutes per 5K and Meg averages 29 minutes with a standard deviation of 4 minutes per 5K. What is the probability that their combined times will be more than an hour?
normalcdf(60, 1000, 52, 5) = .055
According to government data, 20% of employed women have never been married. 25 employed women are selected at random. Find the probability that the number of employed women who have never been married is between 1 and 6.
binomcdf(25,.2, 6) - binompdf(25, .2, 0) = .776
According to government data, 20% of employed women have never been married. 25 employed women are selected at random. Find the probability that the number of employed women who have never been married is greater than 3.
1 - binomcdf(25, .2, 3) = .766
Grace has a history of making her free throws 85% of the time. What is the probability that she will miss her first free throw on her 5th try or after in a game?
1 - geometcdf(.15, 4) = .522
Mr. Woyna plans on racing (beating) Meg in the Lisle 5K. If Mr. Woyna averages 23 minutes with a standard deviation of 3 minutes per 5K and Meg averages 29 minutes with a standard deviation of 4 minutes per 5K. What is the probability that Mr. Woyna wins?
normalcdf(-10000, 0, -6, 5) = .8849 or
normalcdf(0, 1000, 6, 5)
88.5%....