Statistics Final 1/3

Ace your homework & exams now with Quizwiz!

Find the area under the standard normal distribution curve between z = 0 and z = 2.16

- 6.1 - Use Table E - Between = Subtract both Z-Values = .4846

Find the area under the standard normal curve to the right of z = 2.

- 6.1 - Use Table E - To the right = Subtract score from 1 1 - .9772 = .0228

The probability: P(0 < z < 0.97) is 0.3340.

- 6.1 - Use Table E - Z in between = Subtract scores from each other .8340 - .5 = .3340, True

A bottler of drinking water fills plastic bottles with a mean volume of 1001 milliliters (mL) and standard deviation 6 mL. The fill volumes are normally distributed. What proportion of bottles have volumes less than 1001 mL?

- 6.2 - List: μ, σ, -x- ( 1001, 6 1001) - Z = X - μ --------- σ - Less than = Use exact Z-score =.5

The average length of crocodiles in a swamp is 11.5 feet. If the lengths are normally distributed with a standard deviation of 1.7 feet, find the probability that a crocodile is more than 11 feet long

- 6.2 - List: μ, σ, -x- ( 11.5, 1.7, 11) - Z = X - μ --------- σ - More than, Right, = Subtract Z-score from 1 1 - .3859 = .6141

A normal population has a mean μ = 40 and standard deviation σ = 11. What proportion of the population is between 24 and 32?

- 6.2 - List: μ, σ, -x- ( 40, 11, 24 and 32) - Z = X - μ --------- σ - Between = Subtract from each other .2327 - .0735 = .1592

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random, what is the probability that the person will die before the age of 65?

- 6.2 - List: μ, σ, -x- ( 53, 7.5, 65 - Z = X - μ --------- σ - Before, Left, = Use exact Z-score =.9452, or 94.52%

The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 34. A pollster draws a sample of 58 people to interview. What is the probability that the sample mean income is between 38 and 44 (thousands of dollars)?

- 6.3 - Central Limit Theorem - List: *X*, μ, σ, N - Z = *X* - μ -------------- σ/√N - Between = Subtract from each other .7486 - .2514 = .4972

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

- 6.3 - Central Limit Theorem - List: *X*, μ, σ, N - Z = *X* - μ -------------- σ/√N - Between = Subtract from each other .9452 - .7881 = .1571

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33.5 mpg?

- 6.3 - Central Limit Theorem - List: *X*, μ, σ, N - Z = *X* - μ -------------- σ/√N - Greater than, Right = Subtract Z-score from 1 1 - .2546 = .7454

A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 459. Assume the population standard deviation is σ = 103. Construct a 99% confidence interval for the mean mathematics SAT score for the entering freshmen class

- 7.1 - To find Za/2, Subtract Confidence Interval by 1, then divide by two, then subtract from one again. Use Table E afterwards. - List: X, Za/2, σ, N - Use formula for < μ < : X ± Za/2(σ/√N) - - < μ < + = 432.4 < μ < 485.5

The winning team's score in 13 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean.

- 7.2 - Since σ is unknown and s must replace it, (SAMPLE standard deviation, TRUE mean) the T distribution must be used for the confidence interval. To find Ta/2, N-1= DF and Confidence interval % - List: X, Ta/2, s, N - Use formula for < μ < : X ± Ta/2(s/√N) - - < μ < + = 44.6 < μ < 64.0

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?

- 7.3 - Confidence Interval Proportion - To find Za/2, Subtract Confidence Interval by 1, then divide by two, then subtract from one again. Use Table E afterwards. - List: p%, q%, Za/2, N - Use: P% ± Za/2√P%*Q%//N√ - < p < + .621 < p <.779

Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 26 pipes has a standard deviation of 10.6 inches.

-7.4 - Confidence interval for variance - Convert Confidence Interval to A, ( subtract from 1) Then, divide by 2. Answer is x2 Right. Subtract x2 Right by 1 to get x2 Left. Use Chi-Square minus the DF after - List x2right, x2left, σ, N - Use: (N-1)s² (N-1)s² ----------- < ----------- x2 right x2 left


Related study sets

International Financial Statement Analysis Chapter One

View Set

01.02 Driver License Regulation Quiz

View Set

Modern Database Management Chapter 10

View Set

Insurance Flashcards (All Chapters)

View Set

Java Array problems, Java Arrays, Java Chapter 6

View Set

Organizational Behavior Mid-term

View Set