Statistics and Probability Answers

“BLUE PINK”

Situation: A maternity hospital located at the heart of the city is providing nursery kit items for expectant mother clients. The common colors of these items are either pink (for female babies) or blue (for male babies). The hospital management’s concern is the number of each colored item they have to prepare to meet the demands of their clients. On the basis of the previous years’ experience, the management estimates that the probability that any one mother will have a female baby and will be using pink items is .60.

Task: Determine the probability distribution by completing the table from 20 mothers, with    and .

A committee of 4 men and 6 women is to be selected from 7 men and 8 women .if there is a married couple among the 15 people,in how many ways the committee be selected so that the couple are automatically the committee

‘Darshan’ is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.

A. What is the probability of getting fewer than 9,000 hits? 

The paper “Are Babies Normal?” byT. Clemons

and M. Pagano (The American Statistician, Vol. 53,No. 4, pp.

298–302) focused on birth weights of babies. According to

the article, the mean birth weight is 3369 grams (7 pounds

6.5 ounces) with a standard deviation of 581 grams.

a. Identify the population and variable.

b. For samples of size 200, find the mean and standard

deviation all possible sample mean weights.

c. Repeat part (b) for samples of size 400.

An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this particular brand is approximately normal, find the probability that a randomly selected battery of this type will last less than 48 months.

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.

n=10​, p=0.5​, x=7

consider the following joint PDF of X and Y.

F(x,y)= 12x for 0<y<x<1,0<x^2<y<1

find the marginal of X and Y

. Assume that arrivals occur according to a Poisson process with an average

of seven per hour. What is the probability that exactly two customers arrive in the two-hour period

of time between

(a) 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?

(b) 1:00 P.M. and 2:00 P.M. or between 3:00 P.M. and 4:00 P.M. (two separate one-hour periods

that total two hours)?

In southern California, a growing number of individuals pursuing teaching credentials are choosing paid internships over traditional student teaching programs. A group of eight candidates for

three local teaching positions consisted of five who had enrolled in paid internships and three who

enrolled in traditional student teaching programs. All eight candidates appear to be equally qualified, so three are randomly selected to fill the open positions. Let Y be the number of internship

trained candidates who are hired.

(a) Does Y have a binomial or hypergeometric distribution? Why?

(b) Find the probability that two or more internship trained candidates are hired

(c) What are the mean and standard deviation of Y ?.

A corporation is sampling without replacement for n = 3 firms to determine the one from which to

purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are

local and two are not local. Let Y denote the number of nonlocal firms among the three selected.

(a) P(Y = 1).

(b) P(Y ≥ 1).

(c) P(Y ≤ 1).