The distribution of wait times for customers at a certain department of motor vehicles in a large city is skewed to the right with mean 23 minutes and standard deviation 11 minutes. A random sample of 50 customer wait times will be selected. Let x¯W represent the sample mean wait time, in minutes. Which of the following is the best interpretation of P(x¯W>25)≈0.10 ? For a random sample of 50 customer wait times, the probability that the total wait time will be greater than 25 minutes is approximately 0.10.

A For a randomly selected customer from the population, the probability that the total customer wait time will be greater than 25 minutes is approximately 0.10.

B For a randomly selected customer from the population, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.

C For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 23 minutes is approximately 0.10.

D For a random sample of 50 customer wait times, the probability that the sample mean customer wait time will be greater than 25 minutes is approximately 0.10.

A sports magazine reports that the mean number of hot dogs sold by hot dog vendors at a certain sporting event is equal to 150. A random sample of 50 hot dog vendors was selected, and the mean number of hot dogs sold by the vendors at the sporting event was 140. For samples of size 50, which of the following is true about the sampling distribution of the sample mean number of hot dogs sold by hot dog vendors at the sporting event? For all random samples of 50 sporting events, the sample mean will be 150 hot dogs.

A For all random samples of 50 hot dog vendors, the sample mean will be 140 hot dogs.

B The mean of the sampling distribution of the sample mean is 150 hot dogs.

C The mean of the sampling distribution of the sample mean is 140 hot dogs.

D All random samples of 50 hot dog vendors will have a sample mean within 10 hot dogs of the population mean.

A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.3

A 3−7=−4

B 2.7−4.2=−1.5

C 2.73−4.27=0.3

D 4.2−2.7=1.5

Consider two populations of coins, one of pennies and one of quarters. A random sample of 25 pennies was selected, and the mean age of the sample was 32 years. A random sample of 35 quarters was taken, and the mean age of the sample was 19 years.

For the sampling distribution of the difference in sample means, have the conditions for normality been met?

• Yes, the conditions for normality have been met because the distributions of age for the two populations are approximately normal.

  A

• Yes, the conditions for normality have been met because the sample sizes taken from both populations are large enough.

  B

• No, the conditions for normality have not been met because neither sample size is large enough and no information is given about the distributions of the populations.

  C

• No, the conditions for normality have not been met because the sample size for the pennies is not large enough and no information is given about the distributions of the populations.

  D

• No, the conditions for normality have not been met because the sample size for the quarters is not large enough and no information is given about the distributions of the populations.

Compute both a paired t-test and two-sample t-test (for practice) but report the t-value for the correct test.

Buffalo BBQ Restaurant is trying to become more efficient in training its chefs. It is experimenting with two training programs aimed at this objective. Both programs have basic and advanced training modules. The restaurant has provided the following data regarding the two programs after two weeks of implementation:

a. Compute the following performance metrics for each program:

(1) Average hours of employee training per chef, rounded to one decimal place.

Program A:  hrs. per chef

Program B:  hrs. per chef

(2) Average number of mistakes per chef, rounded to one decimal place.

Program A:  mistakes per chef

Program B:  mistakes per chef

b. Which program should the restaurant implement moving forward?

(a) Briefly discuss the binomial probability distribution.

(b) A coin is flipped 12 times: what is the probability of getting:

i. no heads; and)

ii. no more than 3 heads?

Over the past 10 years two golfers have had an ongoing battle as to who the better golfer is. Curtley Weird has won 120 of their 200 matches, while Dave Chilly has won 70 with 10 of them ending in ties. Because Dave is going overseas they decide to play a tournament of five matches to establish once and for all who the better player is.

Find the probabilities that:

(a) Dave wins at least three of the matches;

(b) Curtley wins no more than two games; and

(c) all of the games end in a tie.

(a) Discuss probability, independence and mutual exclusivity, giving examples to illustrate your answer.

i. How many ways are there of choosing a committee of three people from a club of ten?

ii. How many ways are there of selecting from those three people a president, secretary and treasurer?

iii. Illustrate your answer to the second part of the question with a tree diagram.

An ice-cream vendor on the beachfront knows from long experience that the average rate of ice-cream sales is 12 per hour. If, with two hours to go at work, she finds herself with only five ice-creams in stock, what are the probabilities that

(a) she runs out before the end of the day;

(b) she sells exactly what she has in stock by the end of the day without any excess demand after she sells the last one; and

(c) she doesn't sell any?

A company applying for medical aid cover counts that 70 of its 140 male employees smoke. Of the 100 female employees, 20 smoke. What is the probability that an employee chosen at random

(a) is female and smokes; (2)

b) does not smoke; and

(c) is male or smokes?

In a true or false assignment of six questions you are obliged to get at least four correct to pass. If you guess the answers to the questions, what are the probabilities that:

a) you pass; (4)

(b) you get at least 50% of the answers correct; and

(c) you get no more than two correct? (3)

onist claims that he gets 10 calls every five minutes. To demonstrate this to his boss he makes a tape lasting five minutes. What are the probabilities that he gets:

(a) no calls in the five minutes; (2)

(b) less than three calls; and (5)

(c) exactly 10 calls? (

Assume that matric marks are standardised to have a mean of 52% and a standard deviation of 16% (and assume that they have a normal distribution). In a class of 100 students estimate how many of them:

(a) pass (in other words get more than 33,3%);

(b) get A's (more than 80%); and

(c) get B's (between 70% and 80%).

As manager of a company you know that the distribution of completion times for an assembly operation is a normal distribution with a mean of 120 seconds and a standard deviation of 20 seconds. If you have to award bonuses to the top 10% of your workers what time would you use as a cut-off time? [6]

Over the last several years, the average exam grade in social psychology was 86, with a standard deviation of 7. This year, 25 social psychology students have a mean of 82. Are these students different from average social psychology students?

One-tailed or two-tailed?                                            Critical value (with  = .05):

Null Hypothesis (H₀): This sample________________________________________________________

___________________________________________________________________________________

Alternative Hypothesis (H_a): This sample ___________________________________________________

___________________________________________________________________________________

Compute z:

z =                               Reject or fail to reject the null hypothesis?

Interpret result

In cocker spaniels, solid coat color is dominant over spotted coat color. If two heterozygous dogs were crossed to each other, what would be the probability of the following combinations of offspring?

a. A litter of eight pups, two with solid fur and six with spotted fur.

b. A first litter of six pups, four with solid fur and two with spotted fur, and then a second litter of five pups, all with solid fur.

c. A first litter of five pups, the firstborn with solid fur, and then among the next four, three with solid fur and one with spotted fur, and then a second litter of seven pups in which the firstborn is spotted, the second born is spotted, and the remaining five are composed of four solid pups and one spotted pup.

use binominal expansion please

This is problem 8-7 from El-Wakil’s Powerplant Technology book -- air at 14.696 psia, 40 degF, and with 65 percent relative humidity enters the compressor of a gas turbine cycle. The compressor and turbine have the same pressure ratio of 6 and polytropic efficiencies of 0.8 and 0.9, respectively. Water at 60 degF is injected into the compressor exit air, saturating it. Calculate (a) the air temperature after water injection (b) the percent increase in mass flow rate due to water injection, (c) the compressor work in Btus per pound mass of original air, and (d) the compressor work if water is injected during the compression process to the same temperature as (a), in Btus per pound mass of original air. Use a constant c_p = 0.24 Btu/lb_mdegRankine.

3. (a) The amount of orange juice in a ”Minute Made” carton is normally distributed with a mean of 312 millilitres (mL) and a standard deviation of 10 mL. Every ”Minute Made” carton is labelled with the serving size as 300 mL. i. What is the probability that a randomly selected carton has less than the labelled serving? [3 marks] ii. Determine the amount of orange juice in a carton for which only 2% of cartons fall below this amount. [3 marks] iii. Suppose that ”Minute-Made” company sells cartons of orange juice as a pack of 24 to grocery stores. What is the probability that the mean weight of a pack of 24 is in between 305mL and 320mL?

(b) In Singapore, only 40% of the adult citizens have a driving license. Suppose 1000 Singaporean adult citizens are randomly recruited. What is the probability that more than 420 of them possess a driving license? [5 marks]

(c) The San Antonio Spurs basketball team is one of 16 teams who made the NBA playoffs. During the playoffs, the Spurs needs to win over 3 other teams in order to get the championship match. In order to win over an opposing team, the Spurs need to win 4 out of 7 games in a match with the opposing team. Suppose there is a 0.8 probability for the Spurs to win a game. What is the probability that the Spurs can get to the championship match? [5 marks]

An educational psychologist wants to know if length of time and type of training affect learning simple fractions. Fifth graders were randomly selected and assigned to different times (from 1 to 3 hours) and different teaching conditions (old method vs. meaningful method). All students were then tested on the "fractions" subtest of a standard arithmetic test. What can the psychologist conclude with α = 0.01?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Train: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Time: p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0
Interaction: p-value =  ; Decision:

Write a program in c++ that prompts the user to input a coin collection of number of quarters, dimes, nickels

and pennies. The program should then convert the coin collection into currency value as dollars. The

coin values should all be whole numbers and the resulting currency value should be displayed with two

decimals. An example of user interaction is as follows:

Coin Convertor

Enter number of quarters:

3

Enter number of dimes:

1

Enter number of nickels:

4

Enter number of pennies:

12

3 quarters(s), 1 dime(s), 4 nickel(s), and 12 penny(ies) is equal to $1.17

First analyze the problem and write the spec in the order of NARRATIVE, INPUT, OUTPUT, CONSTANTS,

CONSTRAINTS, and OPERATIONS, and then code the program according to the spec. Place the spec at

the top of cpp file as comments. The run-time interaction should be formatted exactly as illustrated

above. The constant values 100, 25, 10, and 5 should each be named constant of integer type.

Grading Scale:

Spec is correct and agrees with code

4

Use meaningful variable names

1

Use named constants

2

Code is properly formatted

1

Program compiles and runs correctly

5

Output is formatted properly (or as required) with two decimal

places

2

Total

15

please help.