BUAL 2650 Gupta Exam 1& 2 | Q&A Latest Update
2025/2026 | 100% PASS
In a manufacturing process, a random sample of 9 manufactured bolts has a
mean length of 3inches with a variance of .09 and is normally distributed. What is
the 90 percent confidence interval for the true mean length of the manufactured
bolt? [x ̄ ± tα/2, n−1(s/n−−√)]= [3±1.86(.3/3)]=[3±.186]=[2.814, 3.186]
2.8140 to 3.1860
In a manufacturing process, a random sample of 36 manufactured bolts has a
mean length of 3inches with a standard deviation of .3 inches. What is the 99
percent confidence interval for the true mean length of the manufactured bolt?
[x±tα/2,n−1(s/n−−√)]=[3±2.719(.3/6)]=[3±.136]=[2.864, 3.136]
2.864 to 3.136
In a manufacturing process, we are interested in measuring the average length of
a certain type of bolt. Past data indicate that the standard deviation is .25 inches.
How many manufactured bolts should be sampled in order to make us 95 percent
confident that the sample mean bolt length is within .02 inches of the true mean
bolt length? n = [(zα/2 × s)/E]2 = [(1.96 × .25)/.02]2 = 600.25 = 601
601
Rejecting a true null hypothesis is called a ________ error.
type 1
A recent study conducted by the state government attempts to determine whether
the voting publicsupports a further increase in cigarette taxes. The opinion poll
recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in
favor of an increase in cigarette taxes. The stategovernment would like to decide
if there is enough evidence to establish whether the proportion ofcitizens
supporting an increase in cigarette taxes is significantly greater than .66. Identify
the null hypothesis
p ≤ .66
In testing H0: μ = 23; versus HA: μ > 23 using the critical value rule, when x x̄ ̄=
26, s = 6,and n = 20, what is the value of the test statistic? Assume that the
population from which thesample is selected is normally distributed.
When testing a hypothesis about a single mean, if the sample size is 51 and the
population standard deviation is known, the correct test statistic to use is
________.
z
It is appropriate to use the uniform distribution to describe a continuous random
variable x when
relative frequencies of all possible values of x are about the same.
The normal approximation of the binomial distribution is appropriate when
np ≥ 5 and n(1 − p) ≥ 5.
The fill weight of a certain brand of adult cereal is normally distributed with a
mean of 910 grams and a standard deviation of 5 grams. We calculated the value
of z for a specific box of this brand of cereal, and the z value was negative. This
negative z value indicates that
, the fill weight is less than 910 grams.
Which of the following statements is not a property of the normal probability
distribution?
95.44 percent of all possible observed values of the random variable x are within plus or
minusthree standard deviations of the population mean.
If the random variable x is normally distributed, ______ percent of all possible
observed values of x will be within three standard deviations of the mean
99.73
The z value tells us the number of ________ that a value of x is from the mean
standard deviations
A continuous probability distribution having a rectangular shape, where the
probability is evenly distributed over an interval of numbers is a(n) ________
distribution.
uniform
The specific shape of each normal distribution is determined by its ________ and
________.
mean, standard deviation.
The area under the curve of a valid continuous probability distribution must
________.
equal 1
______ values of the standard deviation result in a normal curve that is wider and
flatter.
Larger
The mean of a standard normal distribution is always equal to ________.
0
Given that the length an athlete throws a hammer is a normal random variable
with mean 50 feet and standard deviation 5 feet, what is the probability he throws
it no less than 55 feet? Z = (55 − 50)/5 = 1P(X ≥ 55) = 1 − .8412 = .1587
.1587
What is the probability that a standard normal random variable will be between .3
and 3.2?
.3814
For nonnormal populations, as the sample size (n) ________, the distribution of
sample meansapproaches a(n) ________ distribution.
increases, normal
________ says that if the sample size is sufficiently large, then the sample means
are approximatelynormally distributed.
The Central Limit Theorem
Find P(x ̄ < 35) if μ = 40, σx = 16, n = 16.
.1056
Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16
ounces and astandard deviation of .2 ounces. The weights of the sugar packages
are normally distributed. What isthe probability that 16 randomly selected
packages will have a weight in excess of 16.075 ounces? P[z > (16.075 −
16)/(.2/√16)] = P(z > 1.5) = 1.00 − .9332 = .0668
.0688
Find P(x ̄> 172), if μ = 175 and σ2 (variance) = 9. z=(172 − 175)/9-
√=−1P(x>172)=1.00 − .1587
.8413
The exact spread of the t distribution depends on the ________.
number of degrees of freedom
2025/2026 | 100% PASS
In a manufacturing process, a random sample of 9 manufactured bolts has a
mean length of 3inches with a variance of .09 and is normally distributed. What is
the 90 percent confidence interval for the true mean length of the manufactured
bolt? [x ̄ ± tα/2, n−1(s/n−−√)]= [3±1.86(.3/3)]=[3±.186]=[2.814, 3.186]
2.8140 to 3.1860
In a manufacturing process, a random sample of 36 manufactured bolts has a
mean length of 3inches with a standard deviation of .3 inches. What is the 99
percent confidence interval for the true mean length of the manufactured bolt?
[x±tα/2,n−1(s/n−−√)]=[3±2.719(.3/6)]=[3±.136]=[2.864, 3.136]
2.864 to 3.136
In a manufacturing process, we are interested in measuring the average length of
a certain type of bolt. Past data indicate that the standard deviation is .25 inches.
How many manufactured bolts should be sampled in order to make us 95 percent
confident that the sample mean bolt length is within .02 inches of the true mean
bolt length? n = [(zα/2 × s)/E]2 = [(1.96 × .25)/.02]2 = 600.25 = 601
601
Rejecting a true null hypothesis is called a ________ error.
type 1
A recent study conducted by the state government attempts to determine whether
the voting publicsupports a further increase in cigarette taxes. The opinion poll
recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in
favor of an increase in cigarette taxes. The stategovernment would like to decide
if there is enough evidence to establish whether the proportion ofcitizens
supporting an increase in cigarette taxes is significantly greater than .66. Identify
the null hypothesis
p ≤ .66
In testing H0: μ = 23; versus HA: μ > 23 using the critical value rule, when x x̄ ̄=
26, s = 6,and n = 20, what is the value of the test statistic? Assume that the
population from which thesample is selected is normally distributed.
When testing a hypothesis about a single mean, if the sample size is 51 and the
population standard deviation is known, the correct test statistic to use is
________.
z
It is appropriate to use the uniform distribution to describe a continuous random
variable x when
relative frequencies of all possible values of x are about the same.
The normal approximation of the binomial distribution is appropriate when
np ≥ 5 and n(1 − p) ≥ 5.
The fill weight of a certain brand of adult cereal is normally distributed with a
mean of 910 grams and a standard deviation of 5 grams. We calculated the value
of z for a specific box of this brand of cereal, and the z value was negative. This
negative z value indicates that
, the fill weight is less than 910 grams.
Which of the following statements is not a property of the normal probability
distribution?
95.44 percent of all possible observed values of the random variable x are within plus or
minusthree standard deviations of the population mean.
If the random variable x is normally distributed, ______ percent of all possible
observed values of x will be within three standard deviations of the mean
99.73
The z value tells us the number of ________ that a value of x is from the mean
standard deviations
A continuous probability distribution having a rectangular shape, where the
probability is evenly distributed over an interval of numbers is a(n) ________
distribution.
uniform
The specific shape of each normal distribution is determined by its ________ and
________.
mean, standard deviation.
The area under the curve of a valid continuous probability distribution must
________.
equal 1
______ values of the standard deviation result in a normal curve that is wider and
flatter.
Larger
The mean of a standard normal distribution is always equal to ________.
0
Given that the length an athlete throws a hammer is a normal random variable
with mean 50 feet and standard deviation 5 feet, what is the probability he throws
it no less than 55 feet? Z = (55 − 50)/5 = 1P(X ≥ 55) = 1 − .8412 = .1587
.1587
What is the probability that a standard normal random variable will be between .3
and 3.2?
.3814
For nonnormal populations, as the sample size (n) ________, the distribution of
sample meansapproaches a(n) ________ distribution.
increases, normal
________ says that if the sample size is sufficiently large, then the sample means
are approximatelynormally distributed.
The Central Limit Theorem
Find P(x ̄ < 35) if μ = 40, σx = 16, n = 16.
.1056
Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16
ounces and astandard deviation of .2 ounces. The weights of the sugar packages
are normally distributed. What isthe probability that 16 randomly selected
packages will have a weight in excess of 16.075 ounces? P[z > (16.075 −
16)/(.2/√16)] = P(z > 1.5) = 1.00 − .9332 = .0668
.0688
Find P(x ̄> 172), if μ = 175 and σ2 (variance) = 9. z=(172 − 175)/9-
√=−1P(x>172)=1.00 − .1587
.8413
The exact spread of the t distribution depends on the ________.
number of degrees of freedom
