Statistics and Probability Answers

In order to test a dice for fairness, it is thrown repeatedly until a 6 appears. How many throws will you need in order to start suspecting that the dice is probably biased? (So, how many throws will you need with no 6 till you will start believing that there is a problem with the dice?

In a store, an average of 10 customers enters per hour. What is the probability that at most 80 customers enter the store during a 10 hour day?

An airline, 100 seats
For each customer with a ticket: P (absent) = 0.02

a.) If the absence of different passenger are independent events. What is the law of the random variable x = nb of passenger missing a flight.

b.) how do you approach this law? (with steps)

I need to determine the value of z so that the area under the standard normal curve in the right tail is .0505.

Also, finding the area under the standard normal from z=0 to z= -3.75. Is there such a value or is it approx 0?

Two bags A and B contain 4 white 3 black balls and 2 white and 2 black balls respectively. From bag A two balls
are transferred to bag B. Find the probability of drawing
(a) 2 white balls from bag B ?
(b) 2 black balls from bag B ?
(c) 1 white & 1 black ball from bag B ?

1. An LU professor is interested in whether there is a difference between undergraduate students and graduate students in the amount of time spent praying each day. The professor gathers information from random samples of undergraduate and graduate students on the LU campus. The amount of time praying is normally distributed and is measured on an interval/ratio scale.
Graduate Undergraduate
15 9
17 11
10 9
13 6
11 5
17 6


b. Is this a one- or two tailed test?
One-tailed test

c. Identify H0 and Ha for this study.

PROBLEM 1
The (rounded) average price for a box of cookies obtained from 28 bakeries is listed below:

40 23 11 20 22 20 45 15 28 22
22 18 72 19 22 28 27 19 23 46
45 15 30 10 56 15 17 59

a. Construct a grouped frequency distribution and a cumulative frequency distribution with 6 classes.
Note: give a brief explanation by specifying the covered steps.

Grouped Frequency Distribution
Step 1. Find Range
Step 2. Compute classes’ width
Step 3. Create class boundaries
Step 4. Tally the data and find the numerical frequencies from the tally

Cumulative Frequency Distribution
Step 1. Find Range
Step 2. Compute classes’ width
Step 3. Find the frequencies and the corresponding percentage

b. Use Excel to construct a Histogram. (Tools  Data Analysis  Histogram  for input range select the given values, for the bin range select the classes upper boundaries values  check Chart Output).

what are the chances of flipping 4 heads in a row with a penny

A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).


What is the Z critical value (Z cv ) using a 0.05 alpha level?

Should H0 be rejected? What should the researcher conclude?

Determine the 95 % confidence interval for the population mean, based on the sample mean.

In a certain geographic location, 25% of the wage earners have a college degree and 75% do not. Of those who have a college degree, 5% earn more than $100,000 a year. Of those who do not have a college degree, 2% earn more than $100,000 a year. If a wage earner is selected at random, find the probability that she or he earns more than $100,000 a year.