standard deviation

Show all work in the space provided. Be sure to write up your process in a logical and coherent manner. You will be graded not only on your answer, but on your presentation and communication as well. Save your completed assignment as a single pdf and upload it to the appropriate Assignment folder in D2L.
1.The speeds of vehicles on a freeway were observed by radar over a two-hour period. The results revealed anearly normal distribution, with a mean speed of 59 mph and a standard deviation of 6 mph. Use the 68-95-99.7 rule to find the percent in each category. Show the values used to determine your answer.
a.(2 pts) What percent of cars drive slower than 47 miles per hour?
b.(2 pts) What percent of cars drive between 53 and 65 miles per hour?
c.(2 pts) What percent of cars drive between 47 and 65 miles per hour?
2.(2 pts) Under what conditions is a distribution likely to be normal? **Just the 2 big features!
3.(2 pts) A particular outcome has a z-score/standard score of -1.7. What does this mean? Would you considerthe outcome to be unusual?
4.(2 pts) Scores on the quantitative portion of an exam are normally distributed and have a mean of 565 and astandard deviation of 140. What percentile is a score of 400? Show the Excel command, and round thedecimal answer to 4 decimal places.
5.The number of hours of sleep a person in the US gets is normally distributed with a mean of 8 hours and astandard deviation of 0.5 hours. Show the Excel command used to determine your answer.
a.(2 pts) What percent of people will get at most 7.25 hours of sleep? Round your answer to 4 decimalplaces.
b.(2 pts) What percent of people will get at least 9.25 hours of sleep? Round your answer to 4 decimalplaces.
c.(2 pts) If you get 9.25 hours of sleep, what percentile is that? Round to the nearest whole percent.
d.(2 pts) How many hours of sleep would a person at the 20th percentile get?
e.(3 pts) What is the IQR for the number of hours of sleep people get? Hint!! Q1 is the 25th percentile(since 25% of data values lie below it), and Q3 is the 75th percentile (since 75% of data values lie belowit).
6.(3 pts) Heights of 10 year olds, regardless of gender, closely follow a normal distribution with a mean of 55inches and a standard deviation of 6 inches. The height requirement for Batman the Ride at Six Flags MagicMountain is 54 inches. What percent of 10 year olds cannot go on this ride? Show your work and round youranswer to 4 decimal places. Also write your answer in a complete sentence using a percent rounded to thenearest percent.