Probability
In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities. How many students are not involved in either band or sports? Show how you arrived at your answer.
95
The probability that a person is left-handed is 12%, the probability they have browns eyes is 42%, and the probability they have brown eyes and are left handed is 2%. Is the event of having brown eyes independent of being left handed? Support your answer
Dependent
The heights of the members of a high school class are normally distributed. If the mean height is 65 inches and a height of 72 inches represents the 84th percentile, what is the standard deviation for this distribution?
7
On a standardized examination, Laura received a score of 85, which was exactly 2 standard deviations above the mean. If the standard deviation for the examination is 4, what is the mean for this examination?
54
Slide 1
y = 0.488(1.116)x
Ethan surveyed 20 of his friends to find out what equipment they use to play recorded movies. He found that 12 of his friends have only DVD players, 5 have both DVD players and VCRs, and 2 have neither type of player. The rest of his friends have only VCRs. What is the total number of his friends that have VCRs?
1
A newspaper did a survey of adults and found that 54% of the population as a whole favored stricter gun control laws. They broke down the results along gender lines and found that 65% of women favored stricter laws while only 44% of men favored them. If a person was selected at random, are the events of being a woman and being in favor of stricter gun control laws dependent or independent? Explain.
Dependent
If the mean on a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6, what is the best approximation of the percent of the scores that fall between 54.3 and 63.5?
47.5
Which choice is the margin of error, with a confidence level of 95%, for estimating the proportion of green mini M&Ms in a container, if 21 green mini M&Ms were drawn from the container in a random sample of 100 M&Ms?
0.081
Slide 2
y = 999.9725(1.0493)X , 1,367.
At Andrew Jackson High School, students are only allowed to enroll in AP U.S. History if they have already taken AP World History or AP European History. Out of 825 incoming seniors, 165 took AP World History, 66 took AP European History, and 33 took both. Given this information, determine the probability a randomly selected incoming senior is allowed to enroll in AP U.S. History.
198/825
The number of employees who work nights and weekends at a department store is summarized in the table.
Works Nights Doesn't work Nights
Works Weekends. 8 40
Doesn't work 12 60
Weekends
Let N represent the event "works nights" and let W represent the event "works weekends." Based on the table, are N and W independent events?
Yes they are independent
A survey of the soda drinking habits of the population in a high school revealed the mean number of cans of soda consumed per person per week to be 20 with a standard deviation of 3.5. If a normal distribution is assumed, find an interval that the total number of cans per week approximately 95% of the population of this school will drink. Explain why you selected that interval.
13-27
Elizabeth waited for 6 minutes at the drive thru at her favorite fast-food restaurant the last time she visited. She was upset about having to wait that long and notified the manager. The manager assured her that her experience was very unusual and that it would not happen again. A study of customers commissioned by this restaurant found an approximately normal distribution of results. The mean wait time was 226 seconds and the standard deviation was 38 seconds. Given these data, and using a 95% level of confidence, was Elizabeth’s wait time unusual? Justify your answer.
Interval is 150-302 so 360 is unusual
Slide 3
𝑦=42.52722583+13.85752327ln(𝑥)
There are six apples, five oranges, and one pear in Betty's basket. Her friend takes three pieces of fruit at random without replacement. Determine the probability that all three fruits taken are apples.
1/11
Juan and Filipe practice at the driving range before playing golf. The number of wins and corresponding practice times for each player are shown in the table below.
Juan Wins | Felipe Wins
Short Practice Time 8 10
Long Practice Time 15 12
Given that the practice time was long, determine the exact probability that Filipe wins the next match. Determine whether or not the two events “Filipe wins” and “long practice time” are independent. Justify your answer.
Not independent
The weights of the boxes of animal crackers coming off an assembly line differ slightly and form a normal distribution whose mean is 9.8 ounces and whose standard deviation is 0.6 ounce. Determine the number of boxes of animal crackers in a shipment of 5,000 boxes that are expected to weigh more than 11 ounces.
115
The heights of a group of girls are normally distributed with a mean of 66 inches. If 95% of the heights of these girls are between 63 and 69 inches, what is the standard deviation for this group?
1.5
Slide 4
𝑦=141.91242949+10.45366573ln(𝑥)
Maya is a very good student. The probability that she studies and passes her mathematics test is 17/20 . If the probability that Maya studies is 15/16 , find the probability that Maya passes her mathematics test, given that she has studied.
68/75
The results of a poll of 200 students are shown in the table below:
Techno Rap Country
Female 54 25 27
Male 36 40 18
For this group of students, do these data suggest that gender and preferred music styles are independent of each other? Justify your answer.
Not Independent
difference in means question
Some of the students who did not drink energy drinks read faster than those who did drink energy drinks. 17.7 − 19.1 = −1.4 Differences of -1.4 and less occur 25 or about 10% of the time, so the difference is not unusual.
The results of testing a new drug on 1,000 people with a certain disease found that 510 of them improved when they used the drug. Assume these 1,000 people can be regarded as a random sample from the population of all people with this disease. Based on these results, would it be reasonable to think that more than half of the people with this disease would improve if they used the new drug? Why or why not?
No because the interval is 0.4784-0.5416. The lower bound is less than half.
Slide 5
y = 2.19(3.23)x, x=4.5