The human cannonball and other normal tortures
The human cannon ball has flights that are normally distributed with an average of 150 feet and a standard deviation of 10 feet.
a. If his net is 30 feet long how often does he go to the hospital?
If he wants to go to the hospital less than 5% of the time how wide does his net have to be?
1. Coffee consumption per person per day is normally distributed with an average of 14 oz and a standard deviation of 8 oz. What percentage of people consume more than 20 ounces per day? Design a cup that will hold enough coffee for 80 percent of the coffee drinkers.
2. In Pennsylvania, wind speeds are distributed with a mean of 7.8 mph and a standard deviation of 19 mph. If telephone poles are designed to withstand the wind 99 percent of the time, how much wind must telephone poles be able to handle assuming wind velocity is normally distributed? Using the information given above, explain (prove) why wind is definitely not normally distributed.
3. If we assume that all taxpayers are honest, then the average amount that a person over or under pays her taxes should be zero. Half will overpay by mistake. The other half will underpay. Assume the standard deviation of the mistake is $500 and that the amount of the error is normally distributed. Each year the IRS randomly selects a number of taxpayers for an audit. Last year, Will Notpay was found to have underpaid his taxes by $1,257. He claimed, at the time, that it was an honest mistake. Based on the information provided, should the IRS believe him? Explain why or why not.
4. The recording space left unused at the end of a compact disk is normally distributed with an average of 3 minutes and a standard deviation of 1 minute. Whenever supergroup KISS records an album, they always have a 3.5-minute song ready just in case there is sufficient time at the end of the CD. How often will they get to use the extra song? Suppose they wanted to design a song that would fit at the end of the CD 95 percent of the time. How long should the song be?
5. The Electricity bills for PECO energy residential customers average $25.29 for the month of April. The standard deviation for that month is $18.00. Assuming a normal distribution, what percent of customers will have a bill over $50.00? Using the information above, explain (prove) why April electricity bills can't be normally distributed.
6. In Pennsylvania, where the speed limit is 55 mph, the average speed of all cars on the road is 57.6 mph. Vehicle speed is normally distributed with a standard deviation of 8.3 mph. If a police officer wants to set his radar detector to sound the alarm when it records a driver is one of the fastest 5 percent, what speed should activate the alarm? Will Neverspeed was clocked at 30 mph in a 55 mph zone. He claimed he was moving with traffic. Based on a statistical analysis using the information provided, does this seem reasonable? Explain why or why not.