Purchase Solution

General Statistics

Not what you're looking for?

See attached

Solution Summary

The solution discusses Poisson Distribution, Cummulative Distribution, Probability, Confidence Intervals

Solution Preview

See attached

1) The expected number of accidents in a certain intersection in one day is 1.5.

a) What is a reasonable probability distribution for the number of accidents that occur in a day?
A Poisson distribution with  = 1.5 accident/day.

b) What's the probability that no accidents occur in a given day?
Use Poisson pdf, Prob(no accident) = p(r=0|,T=1)

c) What is the probability that 2 or 3 accidents occur in a given day?
Prob (r = 2 or r = 3 ) = p(r=2|,T) + p(r=3|,T)

d) What is the probability of 1.5 accidents on a given day?
Zero. The number of accidents has to be an integer.

e) What is the probability no accidents occur over 3 certain consecutive days?
Prob(r=0 over 3 days) = Prob (no accidents on day 1 and no accidents on day 2 and no accidents on day 3)= Prob(no accidents on day 1) x Prob(no accidents on day 2) x Prob(no accidents on day 3)= p(r=0|,T=1)3

f) Installing a traffic light at the intersection would decrease the expected number of accidents per day to 0.75. Associated with each accident is a 5% chance that someone will sue and win \$1,000,000. What is the expected savings from the traffic light for a day?
Let Z be number of lawsuits lost on a given day.
When 1.5 accidents are expected per day then 1.5x0.05 = 0.075 lawsuits are expected to be lost per day. When 0.75 accidents are expected per day, 0.75x0.05 = 0.0375, lawsuits are expected to be lost per day. As a result, when the rate is 1.5, the expected loss per day is 0.075x\$1,000,000 = \$75,000. When the rate is 0.75, the expected loss per day is 0.0375x\$1,000,000 = \$37,500. The expected savings is \$75,000 - \$37,500 = \$37,500.

2) Earthquakes tend to occur in an area at a rate of one per 24 months. Multiple occurrences of earthquakes in an area are independent.
a) What is a good distribution to model the number earthquakes that occur over a two-year time span ?
A Poisson distribution with  = 1 earthquake per 2 year..

b) What is the probability that 2 or 3 earthquakes in a time span of 2 years
Prob (r = 2 or r = 3 ) = p(r=2|,T) + p(r=3|,T)

c) How many earthquakes would you expect to see in a time span of 3 years.
1.5 (= rate per 2 years * 1.5 = rate per 3 years.)

d) Suppose there was ...

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.