Math 04/17

The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds

A-what is the area between 415 pounds and the mean of 400 pounds?

B-What is the area between the mean and 395 pounds?

C- What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

The time patrons at the Grande Dunes Hotel in the Bahamas spend waiting for an elevator follows a uniform distribution between 0 and 3.5 minutes.

A- Show that the area under the curve is 1.00.

B- How long does the typical patron wait for elevator service?

C- What is the standard deviation of the waiting time?

D- What present of the patrons wait for less than a minute?

E- What present of the patrons wait more than 2 minutes?

The accounting department at Weston Materials Inc. a national manufacturer of unattached garages, reports that takes it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.

A- Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?

B- What percent of the garages take between 29 hours and 34 hours to erect?

C- What percent of the garages take 28.7 hours or less to erect?

D- Of the garages, 5% take how many hours or more to erect?

The annual commons earned by sales representatives of machine products Inc. , A manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5000.

A- What % of the sales representatives earn more than $42,000 per year?

B- What % of the sales representatives earn between $32,000 and $42,000?

C- What % of the sales representatives earn between $32000 and $35000?

D- The sales manager wants to award the sales representatives who earn the largest commission a bonus of $1000; He can award a bonus to 20% of the representatives. What is the cutoff point between those who earn a bonus and those who do not?

Listed below are 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments.

Id Number Dealer ID Number Dealer ID Number Dealer

00 Dave White Acura 11 Thayer Chevrolet/Toyota 23 Kistler Ford Inc.

01 Autofair Nissan 12 Spurgeaon Chev. Motor sales 24 Lexus of Toledo

02 Autofair of Toyota/Suzuki 13 Dunn Chev. 25 Mathews Ford Oregon, Inc

03 Gerorge Ball’s Buick GMC 14 Don Scott Chev. 26 Northtowne Chev.

04 Yark Automotive Group 15 Dave Whites Chev. 27 Quality Ford Sales, Inc

05 Bob Schmidt Chev. 16 Dick Wilson Hyundai 28 Rouen Chrysler Jeep Eagle

06 Bowling Green Lin/Mer 17 Doyle Pontiac Buick 29 Saturn of Toledo

07 Brondes Ford 18 Franklin Park Lincoln Mer. 30 Ed Schmidt Jeep Eagle

08 Brown Honda 19 Genoa Motors 31 Southside Lincoln Mercury

09 Brown Mazda 20 Great Lakes Ford Nissan 32 valiton Chysler

10 Charlie’s Dodge 21 Grogan Towne Chrysler 33 Vin Drivers

22 Hatfield Motor Sales 34 Whitman Ford

A- We want to select a random sample of five dealers. The random numbers are: 05, 20, 59, 21, 31, 28, 49, 38, 66, 08, 29, and 02. Which dealer would be include in the sample?

B- Use the table of random numbers to select your own sample of five dealers.

C- A sample is to consist of every seventh dealer. The number 04 is selected as the starting point. Which dealers are included in the sample?

A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Complete the probability the sample mean is:

A-Less than 74

B- Between 74 & 76

C- Between 76 and 80

D- Greater than 77

According to an IRS study, It takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers.

A- What is the standard error of the mean is this example?

B- What is the likelihood the sample mean is greater than 320 minutes?

C- What is the likelihood the sample mean is between 320 and 350 minutes?

D- What is the likelihood the sample mean is greater than 350 Minutes?

In the department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.

A- Commute the standard error of the sample mean.

B- What is the chance HLI will find a sample mean between 5 and 6 hours?

C- Calculate the probability that the sample mean will be between 5.3 and 5.7 hours.

D- How strange would it be to obtain a sample mean greater than 6.5 hours?

Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with the population standard deviation of 2.44 words per essay. For her 10 am section of 40 students, the mean number of misspelled words was 6.05. Construct a 95% confidence interval for the mean number of misspelled words in the population of student essays.

Schadex Silkscreen printing Inc. purchases plastic cups on which to print logos for sporting events, promos, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random a sample of 300 cups. He found 15 to be defective.

A- What is the estimated proportion defective in the population?

B- Develop a 955 confidence interval for the proportion defective.

C- Zach has an agreement with his supplier that he is to return lots that are 10% or more defective. Should he return this lot? Explain your decision.

A recent survey of 50 executive who were laid off during a recent recession reveled it took a mean of 26 weeks for them to find another position. The standard deviation of the sample was 6.2 weeks. Construct a 95% confidence interval for the population mean. Is it reasonable that the population mean is 28 weeks? Justify your answer.

The manufacture of a new line of ink-jet printers would like to include as part of its advertising the number of pages a user can from a print cartridge. A sample of 10 cartridge revealed the following number of pages printed.

2698 2028 2474 2395 2372 2475 1927 3006 2334 2379

A- What is the point estimate of the population mean?

B- Develop a 95% confidence interval for population mean.

The Tennessee Tourism institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35% of visitors are campers. How large a sample would you take to estimate at 95% confidence level the population proportion with an allowable error of 2%?