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Stat: 2-2
#4: Determine the area under the standard normal curve that lies to the left of (a) Z = 1.72,
(b) Z = 0.66, (c) Z = 0.71, and (d) Z = 0.01.
(a) The area to the left of Z = 1.72 is _____.
(Round to four decimal places asneeded.)
(b) The area to the left of Z = 0.66 is _____.
(Round to four decimal places as needed.)
(c) The area to the left of Z = 0.71 is _____.
(Round to four decimal places as needed.)
(d) The area to the left of Z = 0.01 is _____.
(Round to four decimal places as needed.)
#5) Determine the area under the standard normal curve that lies between (a) Z = -1.55 and
Z = 1.55, (b) Z = – 2.75 and Z = 0, and (c) Z = -1.43 and Z = -0.92.
(a) The area that lies between Z = – 1.55 and Z = 1.55 is _____.
(Round to four decimal places as needed.)
(b) The area that lies between Z = – 2.75 and Z = 0 is _____.
(Round to four decimal places as needed.)
(c) The area that lies between Z = – 1.43Z and Z = – 0.92Z is _____.
(Round to four decimal places as needed.)
#6) Determine the total area under the standard normal curve in parts (a) through (c)
below.
(a) Find the area under the normal curve to the left of z = −2 plus the area under the
normal curve to the right of z = 22.
The combined area is 0.04550.0455.
(Round to four decimal places as needed.)
(b) Find the area under the normal curve to the left of z = − 1.52 plus the area under the
normal curve to the right of z = 2.52.
The combined area is _____.
(Round to four decimal places as needed.)
(c) Find the area under the normal curve to the left of z = – 0.25 plus the area under the
normal curve to the right of z = 1.40.
The combined area is _____.
(Round to four decimal places as needed.)
#9) The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline
mileage is approximately normally distributed with a standard deviation of 3.2 miles per
gallon. (a) What proportion of hybrids gets over 60 miles per gallon? (b) What proportion
of hybrids gets 53 miles per gallon or less? (c) What proportion of hybrids get between 58
and 62 miles per gallon? (d) What is the probability that a random selected hybrid gets less
than 45 miles per gallon?
(a) The proportion of hybrids that gets over 60 miles per gallon is _____.
(Round to four decimal places as needed.)
(b) The proportion of hybrids that gets 53 miles per gallon or less is _____.
(Round to four decimal places as needed.)
(c) The proportion of hybrids that gets between 58 and 62 miles per gallon is
_____.
(Round to four decimal places as needed.)
(d) The probability that a randomly selected hybrid gets less than 45 miles per gallon is
_____.
(Round to four decimal places as needed.)
# 11) Suppose the lengths of the pregnancies of a certain animal are approximately
normally distributed with mean μ = 125 days and standard deviation σ = 12 days.
(a) What is the probability that a randomly selected pregnancy lasts less than 121 days?
The probability that a randomly selected pregnancy lasts less than 121 days is
approximately _____. (Round to four decimal places as needed.)
(b) What is the probability that a random sample of 13 pregnancies has a mean gestation
period of 121 days or less?
The probability that the mean of a random sample of 13 pregnancies is less than 121
days is approximately _____. (Round to four decimal places as needed.)
(c) What is the probability that a random sample of 37 pregnancies has a mean gestation
period of 121 days or less?
The probability that the mean of a random sample of 37 pregnancies is less than 121
days is approximately _____. (Round to four decimal places as needed.)
#13) Describe the sampling distribution of pˆ. Assume the size of the population is 25,000.
N = 900,
p = 0.1
(a) Determine the mean of the sampling distribution of pˆ. μˆp = _____
(Round to one decimal place as needed.)
(b) Determine the standard deviation of the sampling distribution of pˆ. σˆp = _____.
(Round to three decimal places as needed.)
#14) Suppose a simple random sample of size n=125 is obtained from a population whose
size is N = 30,000 and whose population proportion with a specified characteristic is p
equals 0.4.
(a) Determine the mean of the sampling distribution pˆ.
μˆp = _____ (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution pˆ.
σˆp = _____. (Round to six decimal places as needed.)
(b) What is the probability of obtaining x = 55 or more individuals with the characteristic?
That is, what is P(pˆ ≥ 0.44)?
P(pˆ ≥ 0.44) = _____. (Round to four decimal places as needed.)
(c) What is the probability of obtaining x = 40 or fewer individuals with the characteristic?
That is, what is P(pˆ ≤ 0.32)?
P(pˆ ≤ 0.32) = _____ (Round to four decimal places as needed.)
2-3 Journal:
Using the Journal Dataset, consider the variable DP05 (days with precipitation that is more than
05 tenths of an inch). This is the number of days in each month that had 0.5 inches or more of
precipitation. For example, a value of 3 in DP05 means that during three days of that month, it
rained or snowed (equivalent) more than half an inch.
Draw a histogram of DP05. Does DP05 have an approximately normal distribution? Does it
have an obvious skew (left or right) and any obvious outliers? If an analysis requires that DP05
have a normal distribution, do you think that your results will be valid?
Now consider the variable EMXP (extreme maximum precipitation). That is the extreme
precipitation in each month, in tenths of a millimeter. For example, a value of 300 in EMXP
means that it rained 30 millimeters on the rainiest day of that month.
Draw a histogram of EMXP. Does EMXP have an approximately normal distribution? Does it
have an obvious skew (left or right) and any obvious outliers? If an analysis requires that EMXP
have a normal distribution, do you think that your results will be valid?
Stat 3-2
#3) Construct a confidence interval of the population proportion at the given level of
confidence. X = 860, n = 1100, 99% confidence
The upper bound of the confidence interval is _____.
(Round to the nearest thousandth as needed.)
The lower bound of the confidence interval is _____.
(Round to the nearest thousandth as needed.)
#5) In a trial of 300 patients who received 10-mg doses of a drug daily, 45 reported
headache as a side effect. Use this information to complete parts (a) through (d) below.
(a) Obtain a point estimate for the population proportion of patients who received 10-mg
doses of a drug daily and reported headache as a side effect.
pˆ = _____. (Round to two decimal places as needed.)
(b) Construct a 95% confidence interval for the population proportion of patients who
The 95% confidence interval is (_____, _____).
#6) A researcher wishes to estimate the proportion of adults who have high-speed Internet
access. What size sample should be obtained if she wishes the estimate to be within 0.01
with 90% confidence if
(a) she uses a previous estimate of 0.52?
(b) she does not use any prior estimates?
(a) n = _____ (Round up to the nearest integer.)
(b) n = _____ (Round up to the nearest integer.)
#9) Determine the point estimate of the population mean and margin of error for the
confidence interval.
Lower bound is 18, upper bound is 24.
The point estimate of the population mean is _____.
The margin of error for the confidence interval is _____.
#13) The following data represent the asking price of a simple random sample of homes for
sale. Construct a 99% confidence interval with and without the outlier included. Comment
on the effect the outlier has on the confidence interval.
\$189,900
\$143,000
\$149,900
\$170,500
\$279,900
\$205,800
\$212,900
\$147,800
\$219,900
\$154,500
\$187,500
\$264,900
(a) Construct a 99% confidence interval with the outlier included.
(\$_____, \$_____) (Round to the nearest integer as needed.)
(b) Construct a 99% confidence interval with the outlier removed.
(\$_____, \$_____) (Round to the nearest integer as needed.)
#14) A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females.
How many subjects are needed to estimate the mean HDL cholesterol within 44 points with
99% confidence assuming s = 19.4 based on earlier studies? Suppose the doctor would be
content with 90% confidence. How does the decrease in confidence affect the sample size
required?
A 99% confidence level requires _____ subjects. (Round up to the nearest subject.)
A 90 % confidence level requires _____ subjects. (Round up to the nearest subject.)
Stat 4-2
#6) Determine the critical value for a left-tailed test regarding a population proportion at
the α = 0.01 level of significance.
Z = _____. (Round to two decimal places as needed.)
#7) Test the hypothesis using the classical approach and the P-value approach.