Statistics and Probability Answers

Plant scientists developed different varieties of corns that have a rich content of lysine which is a nutritious animal feed. A group of chicks were given this food to test the quality. The distribution of the weight gains (in grams) of these chicks are shown below:

Weight gains (in grams) Frequency

318 - 335 4

336 - 353 5

354 - 371 2

372 - 389 3

390 – 407 2

408 – 425 3

426 - 443 1

Find:

(a) the mean weight gains

(b) the median

(c) the variance for the above frequency intervals

(d) the standard deviation

1.      The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.25. Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion? (1)

1.      A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 60 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. Calculate the confidence interval for the population mean length of the insulation. (2)

2.      The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is no information about the proportion of students who might choose the option. What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.05 of the true proportion? (1)

1.      A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $400 per credit hour. The university system administrators are contemplating charging each student a set fee of $7,000 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a total sample would they need to take? (2)

1.      A college administrator is interested in determining the proportion of students who receive some sort of financial aid. Instead of examining the records for all students, the administrator randomly draws 120 students and finds that 67 of them are receiving financial aid. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid. (1)

2.      In estimating the population mean with the population standard deviation unknown, if the sample size is 17, how many degrees of freedom will there be? (1)

In a town, the probabilities that a family owns a microwave, an air conditioner and a computer are 0.5, 0.6, and 0.8 respectively.

A)If a family is chosen at random from the town, find the probability that the family chosen owns

(i) all three items

(ii) only a microwave and an air conditioner

(iii) none of the three it

1.      To decide what personnel requirements should be enforced, a hospital manager wants to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 48 different 24-hour periods and counts the number of admissions for each. In his sample, the sample mean is 396 and the sample standard deviation is 110. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval. (1)

2.      Using the sample standard deviation as an estimate for the population standard deviation, what size sample should the manager choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 98% reliability? (1)

1. An appliance dealer wants to purchase a combined total of no more than 100 refrigerators, and dishwashers for inventory. Refrigerators weigh 200 pound each, and dishwashers weigh 100 pounds each. The dealer is limited to a total of 12,000 pounds for these two items. A profit of $35 for each refrigerator and $20 on each dishwasher is projected.

(a) Write out the linear programming model by identifying the constraints and the objective function from the description above.

(b) Using a scale of 2 cm to 20 pounds on both axes, construct and shade the region R in which every point satisfies all the constraints.

(c) Based on the graph obtained in (b), determine the corner points and find out the maximum number of refrigerators and dishwashers that the dealer can purchase and sold to make the profit.

A. Construct a scatterplot of the following bivariate data:

1. 

Age of person, in years | 11 | 12 | 13 | 14 | 15 |

Weight (kg)           | 40 | 42 | 38 | 45 | 51 |   

2. 

Age of car, in years  | 11 | 12 | 13 | 14 | 15 | 

Mileage, in km/liter | 40 | 42 | 38 | 45 | 51 | 

B. Identify the dependent and independent variable in each of the following pairs of variables. Write your answer on the space provided

1. The base and the area of the triangle.

Independent Variable:

Dependent Variable:

2. Cost and age of car.

Independent Variable:

Dependent Variable:

3. The age and birth date.

Independent Variable:

Dependent Variable

Survey tests on seIf-concept and on leadership skill were administered to student-leaders. Both tests use a 10-point Likert scale with 10 indicating the highest scores for each test. Scores for students on the tests follow:

Student | A | B | C | D | E | F | G |

Self -Concept | 7.1 | 5.6 | 6.8 | 7.8 | 8.3 | 5.4 | 6.3 |

Leader | 3.4 | 6.0 | 7.8 | 8.8 | 7.0 | 6.5 | 8.3 |

-ship Skill

1. Compute the coeficient of correlation r.

2. Interpret the results in terms of strength and direction of correlation.

3. Find the regression line that will predict the leadership skill if the self-concept score is known