Mat 540 Quiz 4
Quiz 2
Chapters 4 & 5__TEAM A week 5________________________
1) Use the standard normal distribution to find P(-2.25 < z < 1.25).
A) .0122 B) .8821 C) .8944 D) .4878
P(-2.25 < z < 1.25) = F(1.25) - (1 - F(2.25)) = 0.89435 - (1 - 0.987776) = 0.882126
2) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $ 900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above,
a. what is the probability that during a randomly selected month PCE's were between $775.00 and $990.00?
A) .0421 B) .0001 C) .9999 D) .9579
b. what is the probability that during a randomly selected month PCE's …show more content…
were between $375.00 and $590.00?
A) .9579 B) .9999 C) 2.82316E-10 D) .0421
c Find the point in the distribution below which 2.5% of the PCE's fell.
A) $ 682.50 B) $ 602.00 C) $ 802.00 D) $ 17.50
3) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 3.2 millimeters?
A) 1.5 B) 0.4571 C) 0.7111 D) 0.65
4) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 12.5 gallons per minute.
a. What is the probability that at the time the machine is checked it is pumping more than 10.5 gallons per minute?
A) .50 B) .25 C) .7692 D) .667
b.
What is the probability that at the time the machine is checked it is pumping more than 9.0 gallons per minute?
A) .7692 B) .25 C) .50 D) .875
c. What is the probability that at the time the machine is checked it is pumping between 9.5and 10.5 gallons per minute?
A) .50 B) 667 C) .7692 D) .25
5) The time between customer arrivals at a furniture store has an approximate exponential distribution with mean θ = 8.5 minutes.
a. If a customer just arrived, find the probability that the next customer will arrive in the next 5 minutes.
A) .817316 B) .182684 C) .555306 D) .444694
b. .If a customer just arrived, find the probability that the next customer will arrive in the next 3 minutes.
A) .555306 B) .297381 C) .444694 D) .702618
6) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a [pic] period. The director randomly selects 100 different [pic] periods and determines the number of admissions for each. For this sample, [pic] and [pic] Estimate the mean number of admissions per [pic] period with a 99% confidence interval.
A) 16.3 ± 4.120 B) 16.3 ± 1.030 +C) 16.3 ± . 10.3 D) 16.3 ± .
396
7) How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided a sample mean and standard deviation of $18.00 and $2.50, respectively. Use this information to construct a 99% confidence interval for the mean.
A) 18 ± 2.821( 2.50/[pic]) B) 18 ± 3.25( 2.50/[pic])
C) 18 ± 3.106( 2.50/[pic]) D) 18 ± 3.169( 2.50/[pic])
8) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 90% confidence interval for the proportion of college students who prefer drink A: (. 406, . 586). Identify the point estimate for estimating the true proportion of college students who prefer that drink.
A) .0 9 B) . 406 C) . 586 D) . 496 x-bar-ME=.406 + x-bar+ME=.586 = 2(x-bar)=.992 =x-bar=.496
9) A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 99% confidence interval
A) .5625 ± .0 202 B) .4375 ± . 6337 C) .5625 ± . 6337 D) .4375 ± .0 202
10) Suppose the population standard deviation is known to be σ = 150. Calculate the standard error of [pic] when n = 300 and N = 1500.
A) 7.75 B) 6.92 C) 3.87 D) 17.32
Chapters 4 & 5__TEAM A week 5________________________
1) Use the standard normal distribution to find P(-2.25 < z < 1.25).
A) .0122 B) .8821 C) .8944 D) .4878
P(-2.25 < z < 1.25) = F(1.25) - (1 - F(2.25)) = 0.89435 - (1 - 0.987776) = 0.882126
2) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $ 900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above,
a. what is the probability that during a randomly selected month PCE's were between $775.00 and $990.00?
A) .0421 B) .0001 C) .9999 D) .9579
b. what is the probability that during a randomly selected month PCE's …show more content…
were between $375.00 and $590.00?
A) .9579 B) .9999 C) 2.82316E-10 D) .0421
c Find the point in the distribution below which 2.5% of the PCE's fell.
A) $ 682.50 B) $ 602.00 C) $ 802.00 D) $ 17.50
3) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 3.2 millimeters?
A) 1.5 B) 0.4571 C) 0.7111 D) 0.65
4) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 12.5 gallons per minute.
a. What is the probability that at the time the machine is checked it is pumping more than 10.5 gallons per minute?
A) .50 B) .25 C) .7692 D) .667
b.
What is the probability that at the time the machine is checked it is pumping more than 9.0 gallons per minute?
A) .7692 B) .25 C) .50 D) .875
c. What is the probability that at the time the machine is checked it is pumping between 9.5and 10.5 gallons per minute?
A) .50 B) 667 C) .7692 D) .25
5) The time between customer arrivals at a furniture store has an approximate exponential distribution with mean θ = 8.5 minutes.
a. If a customer just arrived, find the probability that the next customer will arrive in the next 5 minutes.
A) .817316 B) .182684 C) .555306 D) .444694
b. .If a customer just arrived, find the probability that the next customer will arrive in the next 3 minutes.
A) .555306 B) .297381 C) .444694 D) .702618
6) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a [pic] period. The director randomly selects 100 different [pic] periods and determines the number of admissions for each. For this sample, [pic] and [pic] Estimate the mean number of admissions per [pic] period with a 99% confidence interval.
A) 16.3 ± 4.120 B) 16.3 ± 1.030 +C) 16.3 ± . 10.3 D) 16.3 ± .
396
7) How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided a sample mean and standard deviation of $18.00 and $2.50, respectively. Use this information to construct a 99% confidence interval for the mean.
A) 18 ± 2.821( 2.50/[pic]) B) 18 ± 3.25( 2.50/[pic])
C) 18 ± 3.106( 2.50/[pic]) D) 18 ± 3.169( 2.50/[pic])
8) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 90% confidence interval for the proportion of college students who prefer drink A: (. 406, . 586). Identify the point estimate for estimating the true proportion of college students who prefer that drink.
A) .0 9 B) . 406 C) . 586 D) . 496 x-bar-ME=.406 + x-bar+ME=.586 = 2(x-bar)=.992 =x-bar=.496
9) A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 99% confidence interval
A) .5625 ± .0 202 B) .4375 ± . 6337 C) .5625 ± . 6337 D) .4375 ± .0 202
10) Suppose the population standard deviation is known to be σ = 150. Calculate the standard error of [pic] when n = 300 and N = 1500.
A) 7.75 B) 6.92 C) 3.87 D) 17.32