2) It is known that at major sporting events only 60% of persons that use the washroom during a break in the action will wash their hands. Assuming that you had observed 14 people leave the washroom, answer the following:
a) The probability that exactly 4 of these people have washed their hands.
b) The probability that more than 10 of these people have washed their hands.
c) The probability that at least 4 of these people will have washed their hands.
d) The expected value for this probability distribution.
It is known that the average age of major league baseball players is 28.3 years with a population standard deviation of 2.8 years. Determine the probability that the average age of 36 randomly selected National League baseball players is less than 27 years of age?
In: Statistics and Probability
A certain tennis player makes a successful first serve 66% of the time. Assume that each serve is independent of the others. If she serves 5 times, what's the probability she gets a) all 5
serves in? b) exactly 4 serves in? c) at least 3 serves in? d) no more than 4 serves in?
a) The probability that she gets all 5 serves in is __________.
(Round to three decimal places as needed.).
b) The probability she gets exactly 4 serves in is ________.
(Round to three decimal places as needed.)
c) The probability she gets at least 3 serves in is ____________.
(Round to three decimal places as needed.)
d) The probability that there are no more than 4 serves in is _____________.
(Round to three decimal places as needed.)
In: Statistics and Probability
The table shows the results of a survey that asked 2850 people whether they were involved in any type of charity work. A person is selected at random from the sample. Find the probability of each event. Give your answers as simplified fractions or as decimals rounded to 3 places.
| Frequently | Occasionally | Not at all | Total | |
| Male | 221 | 456 | 795 | 1472 |
| Female | 207 | 430 | 741 | 1378 |
| Total | 428 | 886 | 1536 | 2850 |
a) What is the probability that the person is frequently or occasionally involved in charity work?
b) What is the probability that the person is female or not involved in charity?
c) What is the probability that the person is male given that they are occasionally involved in charity work?
d) What is the probability that the person is female and frequently involved in charity work?
In: Statistics and Probability
The classrooms at the Redman Academy consist of cramped tables that seat 3 people. The probability of being-left handed is 26%, and left-handed test takers need to sit in the far-left seat, otherwise, they constantly bump elbows with the person next to them causing complaints.
A) What is the probability that no one in a group of 3 students is left-handed?
B) What is the probability that only 1 person in the group of 3 students is left-handed?
C) What is the probability that no one at a table will complain during a test if I randomly seat three students?
D) I have 9 students in my class, 2 of which are left-handed. If I have exactly 3 tables and randomly seat the students, what is the probability of no complaints?
In: Statistics and Probability
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)
a. Compute the probability that a randomly selected peanut M&M is not red.
b. Compute the probability that a randomly selected peanut M&M is yellow or orange.
c. Compute the probability that three randomly selected peanut M&M’s are all orange.
d. If you randomly select six peanut M&M’s, compute that probability that none of them are brown.
e. If you randomly select six peanut M&M’s, compute that probability that at least one of them is brown.
In: Statistics and Probability
An employer is looking to fill some positions, and several college graduates are interviewed. From past experience, we know that the employer will offer second interviews to 65% of the college graduates. Of those graduates offered second interviews, 70% of them will be hired. Only 5% of the college graduates not offered second interviews will be hired.
a) What is the probability of getting offered a second interview and not getting hired?
b) What is the probability of getting hired and not being offered a 2nd interview?
c) What is the probability of a randomly selected graduate (from the original group) being hired?
d) What is the probability of getting hired, given that a second interview was granted?
e) What is the probability of having had a second interview, given that someone was hired?
In: Statistics and Probability
Given a variable with the following population parameters: Mean = 20 Variance = 16 Sample Size = 35
a) What is the probability of obtaining a mean greater the 23?
b) What is the probability of obtaining a mean less than 21?
c) What is the probability of obtaining a mean less than 18.2?
d) What is the probability of obtaining a mean greater than 19.5 and less than 21.2?
e) What is the probability of obtaining a mean greater than 20.5 and less than 21.5?
f) What is the sample mean at which 65% of the data falls at or below?
g) what is the sample mean at which 82% of the data falls at or above?
h) Within what two sample means do 90% of the means fall (i.e symmetrically)?
In: Statistics and Probability
Let X = the distance (in meters) that a small animal moves from its birthplace to the first territorial vacancy it encounters. Suppose that for a specific species X has a uniform distribution with a mean of 75 meters and a standard deviation of 10 meters.
a) What is the probability that the distance is at most 100 m? At most 200m?
b) What is the probability that the distance is between 100m and 200m?
c) What is the probability that the distance exceeds the mean distance?
d) What is the distance exceeded by 15% of the individuals?
e) If the animal has been walking for 100 m, what is the probability that it will have to walk for another 50m?
f) If you observe 15 animals, what is the probability that less than 5 will have to walk more than 100m?
In: Statistics and Probability
A realistic estimate for the probability of an engine failure on a transatlantic fight is 1/14000. Use this probability and the binomial probability formula to find the probabilities of 0, 1, 2, and 3 engine failures for a three engine jet and the probabilities of 0, 1, and 2 engine failures for a two-engine jet. Carry all numbers to as many decimal places as your calculator will display. Use your results and assume that a fight will be completed if at least one engine works. find the probability of a safe fight with a three-engine jet(n=3) and find the probability of a safe fight with a two-engine jet(n=2). Write a report for the federal Aviation Administration that outlines the key issue, and include a recommendation. Support your recommendation with specific results.
In: Statistics and Probability
A market research firm conducts telephone surveys with a 43% historical response rate.
a. What is the probability that in a new sample of 400 telephone numbers, at least 160 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 160/400 = 0.4?
Calculate the standard error to 4 decimals.
Calculate the probability to 4 decimals, showing your steps along
the way.
P( ≥ ) = P(z ≥ ) =
b. If a follow-up study was completed a year later
with only 64 telephone numbers, what is the probability that the
response rate was between 39% and 48%?
Calculate the standard error to 4 decimals.
Calculate the probability to 4 decimals, showing your steps along
the way.
P( ≤ ≤ ) = P( ≤ z
≤ )
= - =
In: Math