Statistics and Probability Answers

A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 20 firemen and found s = 27.2 pounds.

Assuming that the weights of firemen are normally distributed, to test her research hypothesis the statistician would use a chi-square test. In that case, what is the computed test value?

A survey of adults ages 18-29 found that 87% use the internet. You randomly select 100 adults ages 18-29 and ask them if they use the internet.
A) find the probability that exactly 89 people say they use the internet
B) find the probability that at least 89 people say they use the internet
c)Find the probability that fewer than 89 people say they use the internet
d) are any of the probabilities in parts a-c unusual? Explain!

A mandatory
competency test for high school sophomores has a
normal distribution with a mean of 400 and a standard
deviation of 100.
a. The top 3% of students receive $500. What is the
minimum score you would need to receive this
award? 588
6–28Section 6–2Applications of the Normal Distribution 327
6–29
b. The bottom 1.5% of students must go to summer
school. What is the minimum score you would need
to stay out of this group?

Out of 80 customers surveyed, 25 ordered cheese pizza. What is the 99% confidence interval for the true proportion of customers who ordered a cheese pizza?

People of a village randomly tell the truth and tell a lie, nothing is certain.
Suppose, one day you visit the village and ask a person what day it is. He answers,
“Sunday”. What’s the probability of the day actually being Sunday?

In a random sample of 600 smart phines used in Spain, 429 had the android system,107 had window operating system, and the rest had Apple system.
What is the probability the first two have Apple operating system and the third has Window OS?

Gestation Periods. The probability is 0.314 that the gestation
period of a woman will exceed 9 months. In six human
births, what is the probability that the number in which the gestation
period exceeds 9 months is
a. exactly three?
b. exactly five?
c. at least five?
d. between three and five, inclusive?

Recidivism. In the Scientific American article “Reducing
Crime: Rehabilitation is Making a Comeback,” R. Doyle examined
rehabilitation of felons. One aspect of the article discussed
recidivism of juvenile prisoners between 14 and 17 years old, indicating
that 82% of those released in 1994 were rearrested within
3 years. Suppose that, today, six newly released juvenile prisoners
between 14 and 17 years old are selected at random.
a. Assuming that the recidivism rate is the same today as it was
in 1994, determine the probability distribution for the number,
Y , who are rearrested within 3 years.
b. Determine and interpret the mean of Y .
c. If, in fact, exactly two of the six newly released juvenile prisoners
are rearrested within 3 years, would you be inclined to
conclude that the recidivism rate today has decreased from the
82% rate in 1994? Explain your reasoning. Hint: First consider
the probability P(Y = 2).
d. If, in fact, exactly four of the six newly released juvenile prisoners
are rearrested within 3 years, would you be inclined to
conclude that the recidivism rate today has decreased from the
82% rate in 1994? Explain your reasoning.

Lotto. A previous Arizona state lottery called Lotto is
played as follows: The player selects six numbers from the numbers
1–42 and buys a ticket for $1. There are six winning numbers,
which are selected at random from the numbers 1–42. To
win a prize, a Lotto ticket must contain three or more of the winning
numbers. A probability distribution for the number of winning
numbers for a single ticket is shown in the following table.
Number of
winning numbers Probability
0 0.3713060
1 0.4311941
2 0.1684352
3 0.0272219
4 0.0018014
5 0.0000412
6 0.0000002
a. If you buy one Lotto ticket, determine the probability that you
win a prize. Round your answer to three decimal places.

b. If you buy one Lotto ticket per week for a year, determine the
probability that you win a prize at least once in the 52 tries.

The daily sales of Burger Baby restaurants follow the normal distribution with a standard deviation of $4000. What is the probability that the average sales are really $36,000 or less per day? Assume the actual population average is $40,000 per day.

A tire company makes 5000 tires an hour on average with a known standard deviation of 50. A sample is taken last hour and 5100 tires were made. Spell out the null and alternate hypotheses that the mean is different than 5000. Evaluate the hypothesis (Accept or Reject) at the following significance levels: 0.01

One sample has a mean of M = 4 and a second sample has a mean of M = 8. The two samples are combined into a single set of scores.

What is the mean for the combined set if both of the original samples have n = 7 scores?
What is the mean for the combined set if the first sample has n = 3 and the second sample has n = 7?
What is the mean for the combined set if the first sample has n = 7 and the second sample has n = 3?