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MATHS - STATS PROBLEMS WITH SOLUTIONS mcq and essay

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Question;1. (5 points) In a certain town, 4% of people commute to;work by bicycle. If a person is selected randomly from the town, what are the;odds against selecting someone who commutes by bicycle?;A. 1:24;B. 24:1;C. 1:25;D. 24:25;2. (5 points) Among the contestants in a competition are 43;women and 21 men. If 5 winners are randomly selected, what is the probability;that they are all men?;A. 0.02114;B. 0.00267;C. 0.00367;D. 0.13691;3. (5 points) A tourist in France wants to visit 6 different;cities. If the route is randomly selected, what is the probability that she;will visit the cities in alphabetical order?;A. 1/720;B. 1/36;C. 1/6;D. 720;?;4. (5 points) A police department reports that the;probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day;are 0.49, 0.42, 0.06 and 0.03, respectively. What is the mean of the given;probability distribution?;A. 0.63;B. 1.08;C. 0.56;D. 1.5;5. (5 points) The standard deviation for the binomial;distribution with n=40 and p=0.4 is;A. 7.58;B. 3.46;C. 6.73;D. 3.10;6. (5 points) The probability that a person has immunity to;a particular disease is 0.3. Find the mean number who have immunity in samples;of size 18.;A. 5.4;B. 9.0;C. 6.7;D. 7.2;?;7. (5 points) The incomes of trainees at a local mill are;normally distributed with a mean of $1100 and a standard deviation of $120.;What percentage of trainees earn less than $900 a month?;A. 74.5%;B. 9.18%;C. 40.82%;D. 4.75%;8. (5 points) For a standard normal distribution, find the;percentage of data that are between 3 standard deviations below the mean and 2;standard deviation above the mean.;A. 84.00%;B. 65.33%;C. 97.59%;D. 15.74%;?;SHORT ANSWER. Write the word or phrase that best completes;each statement or answers the question. Express percents as decimals. Round;dollar amounts to the nearest cent.;9. (15 points) Most of us hate buying mangos that are picked;too early. Unfortunately, by waiting until the mangos are almost ripe to pick;carries a risk of having 7% of the picked rot upon arrival at the packing;facility. If the packing process is all done by machines without human;inspection to pick out any rotten mangos, what would be the probability of;having at most 2 rotten mangos packed in a box of 12?;10. We have 7 boys and 3 girls in our church choir. There is;an upcoming concert in the local town hall. Unfortunately, we can only have 5;youths in this performance. This performance team of 5 has to by picked randomly;from the crew of 7 boys and 3 girls.;a. (5 points) What is the probability that all 3 girls are;picked in this team of 5?;?;b. (5 points) What is the probability that none of the girls;are picked in this team of 5?;c. (5 points) What is the probability that 2 of the girls;are picked in this team of 5?;11. (15 points) A soda company want to stimulate sales in;this economic climate by giving customers a chance to win a small prize for;every bottle of soda they buy. There is a 20% chance that a customer will find;a picture of a dancing banana () at the bottom of the cap upon opening up a;bottle of soda. The customer can then redeem that bottle cap with this picture;for a small prize. Now, if I buy a 6-pack of soda, what is the probability that;I will win something, i.e., at least win a single small prize?;12. (15 points) A department store manager has decided that;dress code is necessary for team coherence. Team members are required to wear;either blue shirts or red shirts. There are 9 men and 7 women in the team. On a;particular day, 5 men wore blue shirts and 4 other wore red shirts, whereas 4;women wore blue shirts and 3 others wore red shirt. Apply the Addition Rule to;determine the probability of finding men or blue shirts in the team.

 

Paper#61004 | Written in 18-Jul-2015

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