Exam 4: Displaying and Comparing Qualitative Data

A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads on the next flip is

Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap.What is the probability that you find two free ones in a 6-pack?

Traffic accidents Police reports about the traffic accidents they investigated last year indicated that 40% of the accidents involved speeding, 25% involved alcohol, and 10% involved both risk factors. a. What is the probability that an accident involved neither alcohol nor speed? b. Do these two risk factors appear to be independent? Explain.

Cool Off A survey of southern California houses in a given town shows that 70% of the homes have an air conditioning system and 90% of home have at least one ceiling fan. 65% of all homes surveyed had both features. a. What is the probability that a randomly selected home neither feature? b. What is the probability that a randomly selected home has a ceiling fan, given that it already has an air conditioning system? c. Do these two house features appear to be independent? Justify your answer.

Decorate A store sells ornaments for Christmas trees. The prices of the ornaments are roughly normally distributed with a mean of $7.65 and a standard deviation of $1.45. a. What is the probability that a randomly selected ornament will cost more than $10? b. If eight ornaments are randomly selected, what is the probability that exactly 3 of them cost over $10?

Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed. -What are the chances that the kangaroos can jump two nights in a row with no one falling off the bed?

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift. probability 0.10 0.25 0.55 0.10 \# of workers 3 4 5 6 If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)

A sporting goods store announces a “Wheel of Savings” sale. Customers select the merchandise they want to purchase, then at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12 regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount - the merchandise is free! Show your work. -What is the probability that none of the first four customers gets a discount over 20%?

Ten little monkeys were jumping on a bed. There is a 35% chance that one will fall off and bump his head. In the bedroom next door, five kangaroos were jumping on a bed. Being more adept at jumping, there is only a 20% that a kangaroo will fall off the bed. -What are the chances that the kangaroos can get away with jumping on the bed for 4 straight nights until they finally have someone fall off the bed on the 5th night?

A manufacturing firm orders computer chips from three different companies: 10% from Company A; 20% from Company B; and 70% from Company C. Some of the computer chips that are ordered are defective: 4% of chips from Company A are defective; 2% of chips from Company B are defective; and 0.5% of chips from Company C are defective. A worker at the manufacturing firm discovers that a randomly selected computer chip is defective. What is the probability that the computer chip came from Company B? Show your work.

Seatbelts Safety officials hope a public information campaign will increase the use of seatbelts above the current 70% level. Their efforts include running radio and TV ads, putting up billboards, having police officers appear on talk shows, and getting newspapers to indicate whether people injured in accidents were belted in. After several months they check the effectiveness of this campaign with a statewide survey of 560 randomly chosen drivers. 407 of those drivers report that they wear a seatbelt. a. Verify that a Normal model is a good approximation for the binomial model in this situation. b. Does the survey result suggest that the education/advertising campaign was effective? Explain.

Five juniors and four seniors have applied for two open student council positions. School administrators have decided to pick the two new members randomly. What is the probability they are both juniors or both seniors?

Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going through a red light. If 4% have been ticketed for both, what is the probability that a teenage driver has been issued a ticket for speeding but not for running a red light?

The length of a cat's tail is roughly normally distributed with a mean of 5" and a standard deviation of 2". The probability of having a cat with a 3.5" tail or shorter is...

Many school administrators watch enrollment numbers for answers to questions parents ask. Some parents wondered if preferring a particular science course is related to the student's preference in foreign language. Students were surveyed to establish their preference in science and foreign language courses. Does it appear that preferences in science and foreign language are independent? Explain. Chemistry Physics Biology Total French 16 10 8 34 Spanish 35 23 44 102 Total 51 33 52 136

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of customers for a day, and whether they purchase specialty clothes for their pet. -What is the probability that she does not sell a garment until the 7th customer? Show work.

The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy a magazine and thinks that he might be able to use the display space to sell something more profitable. Before making a final decision he decides that for one day he'll keep track of the number of customers and whether or not they buy a magazine. -Surprised by the high number of customers who purchased magazines that day, the owner decided that his 5% estimate must have been too low. How many magazine sales would it have taken to convince you? Justify your answer.

Which two events are most likely to be independent?

A sporting goods store announces a “Wheel of Savings” sale. Customers select the merchandise they want to purchase, then at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12 regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount - the merchandise is free! Show your work. -What is the probability that a customer gets at least a 40% discount?

According to the National Telecommunication and Information Administration, 50.5% of U.S. households had Internet access in 2001. What is the probability that four randomly selected U.S. households all had Internet access in 2001?