stat

STAT 350 (Spring 2017) Homework 4 (20 points) 1

Practice Problems: 5.71 (p.221), 5.73 (p.221), 5.75 (p.221), 5.79 (p.221) (3 pts.) 1. In Illinois, a typical DUI (Driving Under the Influence) offender is a 34-year-old male,

arrested between 11 p.m. and 4 a.m. on a weekend, and has a BAC (blood alcohol content) of 0.16. Eighty-five percent of all drivers arrested in Illinois for driving under the influence are first-time offenders (it is their first time being arrested for DUI). Suppose 40 people arrested for DUI in Illinois are selected at random.

(1 pt.) a) What is the probability that exactly six people are repeat offenders (they are NOT first-

time offenders)? (1 pt.) b) What is the probability that at least two people are repeat offenders? (include at least 3

decimal places in your answer) (0.5 pt.) c) What is the mean of the number of repeat offenders that are arrested? (0.5 pt.) d) What is the standard deviation of the number of repeat offenders that are arrested? Additional Problems: 5.87, 5.93, 5.95 Practice Problems: 5.109 (p. 234) (3 pts.) 2. Buchtal, a manufacturer of ceramic tiles, reports on average 3.9 job-related accidents

per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson.

(1 pt.) a) What is the probability that there are exactly 3 accidents in a year? (0.5 pt.) b) Suppose a half-year is randomly selected. What is the expected number of accidents

in this time period? (0.5 pt.) c) What is the standard deviation of the number of accidents in half a year? (1 pt.) d) If the number of accidents is more than 2 in a half-year, the company insurance carrier

will raise the rates. What is the probability of an increase in the company’s insurance bill?? Additional Problems: 5.119, 5.121 Practice Problems: 6.1 (p.252), 6.3 (p.252) (2 pts.) 3. Determine if each of the following functions are legitimate density curves. Please

graph or sketch each one.

(1 pts.) a) f(x) = 3

5 (5 − 𝑥2) for 0 < x < 2

(1 pts.) b) f(x)= 8

𝑥3 for x>2

(1 pts.) 4. The following function is a density function where k is a constant: f(x) = k(x2 + 3) for

-1 < x < 3. What is the value of k?

STAT 350 (Spring 2017) Homework 4 (20 points) 2

(5.5 pts.) 5. The following function is a legitimate density function: 𝑓(𝑥) = 𝑥+5

16 for 2 < x < 4 and

0 else. (1 pt.) a) Find P(1 ≤ x < 3). (1 pt.) b) What is the expected value? (1 pt.) c) Determine the cdf. (1 pt.) d) Find the 75th percentile. (1 pt.) e) Find the variance. (0.5 pts.) f) Find the standard deviation. Practice Problems: 6.27 (p.267), 6.29 (p.267) (4 pts.) 6. Movie trailers are designed to entice audiences by showing scenes from coming

attractions. Several trailers are usually shown in a theater before the start of the main feature, and most are available via the Internet. The duration of a movie trailer is approximately normal, with mean 150 seconds and standard deviation 30 seconds. Hint: convert all times to seconds.

(1 pt.) a) Find the probability that a randomly selected trailer lasts between 1 minute 59 seconds

and 3 minutes 13 seconds. (1 pt.) b) Any movie trailer that lasts beyond 4 minutes and 10 seconds is considered too long.

What proportion of movie trailers is too long? (1 pt.) c) What length will be in the top 11% of all movie trailers? (1 pt.) d) Find a symmetric interval about the mean such that 97% of all movie trailer durations

lie in this interval. Additional Problems: 6.43, 6.45, 6.47, 6.49 Practice Problems (from the online chapter 6.5): 6.127, 6.129, 6.131 (1.5 pts.) 7. There have been many science conferences and research papers concerning

global warming. Several climate model predictions include higher surface temperatures, rising sea levels, and larger subtropical deserts. Global leaders continue to discuss possible actions to stop or slow these trends. Despite the ominous warnings, a recent survey indicated that only 44% of Americans said that global warming should be a high priority for political leaders and governments. Suppose 250 Americans are selected at random and each is asked if global warming should be a high priority issue. Answer each problem using the normal approximation to the binomial distribution.

(0.5 pt.) a) Is the normal approximate to the binomial appropriate in this situation? Do part b) no

matter what your answer is. (1 pt.) b) Find the approximate probability that at most 110 Americans believe global warming

should be a high priority issue. Remember the continuity correction. Practice Problems: 6.137, 6.139, 6.141, 6.143, 6.145