Download Statistics Test 3 Name: 1. Find the area under the standard normal

Statistics
1.
2.
Test 3
Name:
Find the area under the standard normal distribution
curve for each.
(a)
(a) Between z = −0.19 and z = 1.23.
(b) To the left of z = −1.56.
(b)
(c) To the right of z = −0.38.
(c)
Find each probability using the standard normal distribution curve for each.
(a)
(a) P (−0.09 < z < 2.42)
(b) P (z > −1.68)
(b)
(c) P (z < 0.23)
(c)
3.
4.
Find the indicated z score. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1.
(a)
(a)
(b)
(b)
Use the Standard Normal Distribution to find the requested z value.
(a) Find the z that separates the lower 88% of z scores from the top
(a)
12%
(b)
Find the value of z that represents the 92nd percentile.
(b)
5.
Find the value of z that represents the 45th percentile.
5.
6.
The waiting time in line at a Starschmuchs Coffee is normally distributed with a mean of 3.2 minutes and a standard deviation of 1.3
minutes. Find the probability that a randomly selected customer has
to wait
(a)
Less than 1 minute.
(a)
(b)
more than 2 minutes.
(b)
(c)
between 0.75 minutes and 2 minutes.
(c)
7.
The average yearly precipitation in San Diego is 9.62 inches with a
standard deviation of 4.42 inches and precipitation amounts are normally distributed.
(a)
Find the probability that a randomly selected year will have
precipitation greater than 12 inches.
(a)
(b) Find the probability that five randomly selected years will have
an average precipitation greater than 8 inches.
(b)
(c)
Find the precipitation amount from the distribution of precipitations that represents the 75th percentile.
(c)
8.
Some passengers died when a water taxi sank in Baltimore’s inner
harbor. Men are typically heavier than women and children, so when
loading a water taxi, let’s assume a worst-case scenario in which all
passengers are men. Based on data from the National Health and Nutrition Survey, assume that weights of men are normally distributed
with a mean of 172 lb. and a standard deviation of 29 lb.
(a)
Find the probability that if an individual man is randomly selected, his weight will be greater than 175 lb.
(a)
(b)
Find the probability that 20 men will have a mean weight that
is greater than 175 lb. (so that their total weight exceeds the safe
capacity of 3500 lb.
(b)
9.
The average per capita spending on health care in the United States
is $5274. The standard deviation is $600 and the distribution of health
care spending is approximately normal. Find the limits of the middle
50% of individual health care expenditures.
9.
10.
A prestigious college decides to only take applications from student
who have scored in the top 5% on the SAT test. The SAT scores are
approximately normally distributed with a mean of 490 and a standard
deviation of 70. Find the score that is necessary to obtain in order to
qualify for applying to this college.
10.
11.
Americans ate an average of 25.7 pounds of Krusty-O Cereal each
last year and spent an average of $61.50 per person doing so. If the
standard deviation for consumption is 3.75 pounds and the standard
deviation for the amount spent is $5.89, find the following:
(a) The probability that the sample mean Krusty-O cereal consumption for a random sample of 40 American consumers exceeded 27
pounds.
(a)
(b) The probability that for a random sample of 50, the the average
yearly amount spent on Krusty-O Cereal was between $60.00 and
$100.
(b)
12. Find the critical value zc that corresponds to a 92% confidence interval.
12.
13. First-semester GPAs for a random selection of freshmen at a large university are shown below. Estimate the true mean GPA of the freshman
class with 99% confidence. Assume σ = 0.62 and that the distribution
of first-semester GPAs is normal.
1.9
2.8
2.5
3.1
3.2
3.0
2.7
2.7
2.0
3.8
2.8
3.5
2.9
2.7
3.2
3.8
2.7
2.0
3.0
3.9
3.3
1.9
3.8
2.7
14. Find the critical value tc that corresponds to a 90% interval, assuming
n = 10.
14.
15. The approximate costs for a 30-second spot for various cable networks
in a random selection of cities are shown below. Estimate the true
population mean cost for a 30-second advertisement on cable network
with 90% confidence. Assume the population of costs is approximately
normal.
14
22
55
12
165
13
9
54
15
73
66
55
23
41
30
78
150
16. A university dean of students wishes to estimate the average number
of hours students spend doing homework per week. The standard
deviation from a previous study is 6.2 hours. How large a sample
must be selected if he wants to be 99% confident of finding whether
the true mean differs from the sample mean by 1.5 hours?
16.
17. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the sample standard deviation was 6.6, construct
a 99% confidence interval for the mean score of all students.
17.
18. A study of 35 golfers showed that their average score on a particular
course was 92. The standard deviation of the population is 5. Find
the 95% confidence interval of the mean score for all golfers.
18.
19. A recent study of 75 workers found that 53 people rode the bus to
work each day. Find the 95% confidence interval of the proportion of
all workers who rode the bus to work
19.
20. It is believed that 25% of U.S. homes have a direct satellite television
receiver. How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage
points? How large a sample is necessary if nothing is known about the
proportion?
20.
21. A recent poll showed results from 2000 professionals who interview job
applicants. 26% of them said the biggest interview turnoff is that the
applicant did not make an effort to learn about the job or the company.
A 99% confidence interval estimate was used and the margin of error
was ±3 percentage points. Describe what is meant by the statement
“the margin of error was ±3 percentage points.”