Statistics and Probability Answers

The length of timber cuts are normally distributed with a mean of 95inches. In a random sample of 45 boards, what is the probability that the mean of the sample will be between 94.8 inches and 95.8 inches?

A machine set to fill soup cans with a mean of 20 ounces and a standard deviation of .11 oz. A random sample of 15 cans has a mean of 20.04 oz. Should the machine be reset?

Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 20% of wait times?

A professor records the time (in minutes) that it takes 16 students to complete an exam. Compute the SS, the variance, and the standard deviation assuming the 16 students constitute a population and assuming the 16 students constitute a sample. (Round your answers for variance and standard deviation to two decimal places.)
40 47 28 32
23 42 24 43
13 49 30 37
20 43 38 31
(a) the 16 students constitute a population
SS
variance
standard deviation
min

(b) the 16 students constitute a sample
SS
variance
standard deviation
min

Six sprinters have made it to the Olympic finals in the 100-meter race. In how many different ways can the
gold, silver and bronze medals be awarded (rounded off to zero decimals)?

The table of information was recently collected at De Kuilen High School. Use this information to answer the
questions that follow.
Class Males Females Total
9
th grade 91 101 192
10th grade 95 105 200
11th grade 103 98 201
12th grade 97 101 198
Total 386 405 791
Question 4

What is the probability that a randomly selected student from the school is a 9th grader given that it’s a
male student (rounded off to three decimals)?

Question 5
What is the probability that a randomly selected student from the school is 12th grade or a female (rounded
off to three decimals)?

A planning committee for a major development project must consist six members. There are eight architects
and five engineers available to choose from.
Question 1
In how many different ways can this planning committee be formed (rounded off to zero decimals)?
Question 2
In how many ways can a planning committee be chosen with at least three engineers (rounded off to zero
decimals)? There is at least one architect and one engineer on the planning committee.

a small company has a call center with two phone lines only. an average of 40 people per hour calls in for orders, and it takes an average of 2 minutes to handle a call. interarrival time between call arrivals and time to serve calling customers is on phone are exponentially distributed. if there are more than two customers waiting to be served, a caller gets a busy signal and hangs up. b) (5 points) what is the average time that the phone lines stay idle? c) (10 points) calculate the fraction of the time that the line will be busy? d) (10 points) calculate the average number of customers on hold waiting to be answered

Suppose height to the bottom of clouds is a gaussian random variable X for which mean ax = 4000 m, and standard deviation sx = 1000m. A person bets that cloud height tomorrow will fall in the set A={1000m < Xs 3300m) while a second person bets that height will be satisfied by B= (2000m < Xs 4200m). A third person bets they are both correct. Find the probabilities that each person will win the bet.