Statistics Final 1/3
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
