Statistics and Probability Answers

Two dice are thrown. What is the probability that the sum of dots shown is 4 or 6?

Lengths of pregnancies of humans are normally distributed with a mean of 267 days and a standard deviation of 14 days. Use the Empirical Rule to determine the percentage of women whose pregnancies are between 265 and 295 days.

The next 2 questions refer to the following scenario. Suppose the manager of a pet store wants to determine if there is a difference in the amount of money spent in the store, on average, by owners of dogs vs. owners of cats. Consider dog owners as group 1 and cat owners as group 2. Assume that the population standard deviations are equivalent between groups. Below are the sample data for the nine dog owners and the 9 cat owners. Test the hypothesis at alpha equals 1%.
The hypothesis at Ho: µ1 = µ2 vs. Ha: µ1 ≠ µ2.
Group1 Group 2
36 35.5
19 32.5
24.5 30
27 31.5
20 35.5
35 38
24.5 34.5
23.5 36
27.5 26

15) What is the p-value and test statistic used to test this hypothesis?
a) 0.0162 2.134
b) 0.9961 -2.134
c) 0.0339 3.044
d) 0.0756 3.044
e) 0.0077 -3.044

16) Is there a significant difference in the amount of money spent in the pet store, on average, by owners of dogs vs. c

A discrete random variable X has possible values xi=i^2 i=1,2,3,4,5, which occour with probabilities 0.4 0.25 0.15 0.1 and 0.1 respectively
a) write the probability density fx(x) and probability distrubution Fx(x) functions for X random variable
b)find mean value E[X]

If you engage in a dangerous sport, where you have a 1 in 10 chance of dying, and you do it 25 times. What are your chances of dying?

1 out of 10 people default on their car loans. Last Month a bank approved 50 car loans. Use the Normal Approximation of the Binomial to find the probability atleast three borrowers will default?

1 out of 10 people default on their car loans. Last Month a bank approved 50 car loans. Use the Normal Approximation of the Binomial to find the probability atleast three borrowers will default?

I have a couple of questions for function and Sample mean and CLT. Any question for any of the questions and I'll be grateful!

III. Functions of two random variables, Sample mean, CLT.
1. Let X and Y be independent r.v.’s such that X is uniform r.v over (2,3), and Y is uniform r.v over (1,4).
1.1 Find and sketch the pdf of Z = X + Y.
2. Find
3. 3.1 Consider two r.v.’s X and Y with joint . Determine the pdf of Z = XY.
3.2 Let X and Y be independent such that X is uniform r.v over (0,2), and Y is uniform r.v over (1,3). Find the pdf of Z = XY.

3. Ten independent samples of a random variable X are taken. Determine the expected value and variance of the sample mean if the r. v X is uniformly distributed over (-1,1).
4. A certain component is critical to the operation of an electrical system and must be replaced immediately upon failu

KP Cafeteria coffee is very popular. On average, it sold 10 cups of coffee per
hour. Find the
i. probability that exactly 12 cups of coffee were sold in 2 hours,

1. A biology test consists of 5 true or false questions. A student who sat for the examination tried to answer each question by nearly guessing without reading each statement. The probability of the student scoring exactly 4 correct is?