Statistics and Probability Answers

A beach resort buy a policy to insure against loss of revenues due to major storms in the summer. The policy pays a total of $ 50,000 if there is only one major storms during the summer, a total of $ 100,000 if there are two major storms, and a total payment of $ 200,000 if there are more than two major storms. The number of major storms in one summer is modeled by a Poisson distribution with mean of 0.5 per summer. Find
(a) Find the expected premium for this policy during one summer.
(b) the standard deviation of the cost of providing this insurance for one summer.

A geological study indicates that an exploratory oil well should strike oil with probability 0.2.
(a) What is the probability that the first strike comes on the third well drilled? (b) What assumptions did you make to obtain the answer in (a).
26. At a checkout counter customers arrive at an average of 2 per minute. Find the probability that

suppose that 1 out of 10 plasma televisions shipped with a defective speaker. out of a shipment of n=400 plasma televisions. find the probability (as a %) that there are more than 28 with defective speakers

If women have pulse rates that normally distributed with mean =74 and the standard deviation =12.0, then the probability that one woman randomly selected will have pulse rate less than 68 is approximately?

What is the probability that you will first cut an ace:
a) on the 5th cut?
b) in fewer than 4 cuts?
c) What is the expected waiting time before you cut an ace?

You throw a die repeatedly until you get a 6. What is the probability that you need to throw more than 20 times to get 6?

5. Let X represents the number of computers in an Australian household, for those that own a
computer.

a. Find and interpret the expected number of computers in a randomly selected Australian
household. (2 marks)
b. What is the probability that a randomly selected Australian household will have more than 2
computers?
c. Find V (4X +2). (1 mark)
d. Find E(30X + 20]. (1 mark)

According to the Sleep Foundation, the average night’s sleep is 7 hours. Assume the standard deviation is 0.5 hours and that the probability distribution is normal.
a. What is the probability that a randomly selected person sleeps more than 9 hours?
b. What is the probability that a randomly selected person sleeps 5 hours or less?
c. What is the probability that a randomly selected person sleeps exactly 10 hours?
d. What is the probability that a randomly selected person sleeps more than 7 hours?
e. Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?

Annual income in thousands:(12),(13),(14),(15),(16),(17),(18),(19),(20).
Annual savings in thousands:(0),(0.1),(0.2),(0.2),(0.5),(0.5),(0.6),(0.7),(0.8).
Find the following:
1) equation line y on x
2) equation line x on y
3) find the annual saving when annual income is 25000.
4)find the annual income when annual saving is 550.

A sample of n=400 observations is drawn from a population with mean μ=1,000 and σ=400. Find the following probabilities:

P
( x ¯ ≤ 1030 )
is: