sean and evan are college roommates who have parttime jobs as servers in restaurants. the distribution of sean’s weekly income is approximately normal with mean $225 and standard deviation $25. the distribution of evan’s weekly income is approximately normal with mean $240 and standard deviation $15. assuming their weekly incomes are independent of each other, which of the following is closest to the probability that sean will have a greater income than evan in a randomly selected week?
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get sean and evan are college roommates who have parttime jobs as servers in restaurants. the distribution of sean’s weekly income is approximately normal with mean $225 and standard deviation $25. the distribution of evan’s weekly income is approximately normal with mean $240 and standard deviation $15. assuming their weekly incomes are independent of each other, which of the following is closest to the probability that sean will have a greater income than evan in a randomly selected week? from EN Bilgi.
Sean and Evan are college roommates who have part
Sean and Evan are college roommates who have parttime jobs as servers in restaurants. The distribution of Sean’s weekly income is approximately normal with mean $225 and standard deviation $25. The distribution of Evan’s weekly income is approximately normal with mean $240 and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week? a. 0.67 b. 0.700 c. 0.227 d. 0.303 e. 0.354 None
Asked by djdavis
mathematics answered out
Sean and Evan are college roommates who have parttime jobs as servers in restaurants. The distribution of Sean’s weekly income is approximately normal with mean $225 and standard deviation $25. The distribution of Evan’s weekly income is approximately normal with mean $240 and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?
a. 0.67 b. 0.700 c. 0.227 d. 0.303 e. 0.354 None
6 months ago
Answers
Answer: d. 0.303 Stepbystep explanation:Normal Probability Distribution:Problems of normal distributions can be solved using the zscore formula.In a set with mean and standard deviation , the zscore of a measure X is given by: The Zscore measures how many standard deviations the measure is from the mean. After finding the Zscore, we look at the zscore table and find the pvalue associated with this zscore. This pvalue is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.Subtraction between normal variables:When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.In this question:We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.Distribution of the difference between Sean's and Evan's income:Sean has mean 225, Evan 240. So Sean's standard deviation is of 25, Evan's of 15. So Probability that Sean will have a greater income than Evan in a randomly selected week:Probability of the subtraction being greater than 0, which is 1 subtracted by the pvalue of Z when X = 0. So has a pvalue of 0.6951  0.695 = 0.305.Closest to 0.303, option d.
Answerd by dzahmed
6 months ago 15 5.0
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2019 Stat AP
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AP ® Statistics Exam 2019
SECTION I: Multiple Choice
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.
At a Glance Total Time
1 hour and 30 minutes
Number of Questions 40
Percent of Total Score
50% Writing Instrument Pencil required Electronic Device Graphing calculator expected Instructions
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. Form I Form Code 4PBP4S 90
Formulas begin on page 3.
Questions begin on page 6.
Tables begin on page 42.
2
Formulas
(I)Descriptive Statistics
x i x n 2 1 1 x s x x i n 22 12 12 12 11 11 p n s n s s n n 01 ˆ y b b x 1 2 i i i x x y y b x x 01 b y b x 1 1 i i x y x x y y r n s s 1 y x s b r s 2 2 1 ˆ 2 i i b i y y n s x x
AP Stat Flashcards
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AP Stat
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Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements
are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics
will remain the same for both units of measure?
(A) The mean of the height measurements
(B) The median of the height measurements
(C) The standard deviation of the height measurements
(D) The maximum of the height measurements
(E) The zscores of the height measurements
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E
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A school principal wanted to investigate student opinion about the food served in the school cafeteria. The principal
selected at random samples of 50 firstyear students, 50 secondyear students, 50 thirdyear students, and 50 fourthyear
students to complete a questionnaire. Which of the following best describes the principal's sampling plan?
(A) A stratified random sample
(B) A simple random sample
(C) A cluster sample
(D) A convenience sample
(E) A systematic sample
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A
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1/41 Created by btwinovel
Terms in this set (41)
Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements
are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics
will remain the same for both units of measure?
(A) The mean of the height measurements
(B) The median of the height measurements
(C) The standard deviation of the height measurements
(D) The maximum of the height measurements
(E) The zscores of the height measurements
E
A school principal wanted to investigate student opinion about the food served in the school cafeteria. The principal
selected at random samples of 50 firstyear students, 50 secondyear students, 50 thirdyear students, and 50 fourthyear
students to complete a questionnaire. Which of the following best describes the principal's sampling plan?
(A) A stratified random sample
(B) A simple random sample
(C) A cluster sample
(D) A convenience sample
(E) A systematic sample
A
A candy company produces individually wrapped candies. The quality control manager for the company believes that
the weight of the candies is approximately normally distributed with mean 720 milligrams (mg). If the manager's
belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the
distribution of weights?
(A) 740 mg to 780 mg
(B) 700 mg to 740 mg
(C) 680 mg to 720 mg
(D) 660 mg to 700 mg
(E) 620 mg to 660 mg
B
A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution
is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices
based on the graph?
(A) The mean is greater than the median.
(B) The median is the average of the first quartile and the third quartile.
(C) There are fewer selling prices between the first quartile and the median than there are between the median and the
third quartile.
(D) There are more selling prices that are less than the mean than selling prices that are greater than the mean.
(E) The value of maximum minus third quartile is less than the value of first quartile minus minimum.
E
The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below
shows the distribution of times, in seconds, for the 100 mice.
Which of the following values is closest to the standard deviation of the 100 times?
(A) 2.5 seconds (B) 10 seconds (C) 20 seconds (D) 50 seconds (E) 90 seconds B
If a probability distribution is symmetric, which of the following statements must be true?
(A) The distribution is normal.
(B) The distribution is uniform.
(C) The distribution is bimodal.
(D) The mean of the distribution is equal to the median of the distribution.
(E) The interquartile range of the distribution is equal to the standard deviation of the distribution
D
Let X represent the number on the face that lands up when a fair sixsided number cube is tossed. The expected value
of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair sixsided number cubes will be tossed,
and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the
standard deviation of the resulting sum?
(A) 1.708 (B) 1.848 (C) 2.415 (D) 3.416 (E) 5.835 C
The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades
by the National Hurricane Center. Summary measures are shown below.
Min = 12 Lower quartile = 15 Median = 16 Max = 24 Upper quartile = 18 n = 10
Which of the following statements is true?
(A) The smallest observation is 12 and it is an outlier. No other observations in the data set could be outliers.
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