Assignment:
1. A particular type of water pump fails on the average once every 6,000 hours of operation. Let the random variable x count the number of failures in 6,000 hours.
a.) Find the probability of no failures in 6,000 hours of operation.
b.) Find the variance and the standard deviation for this random variable.
2. ) Assuming that the probability of a child being a boy or a girl are both 0.5, fin the probability that a family of five children will have exactly three boys.
3.) Based on historical records, the owner of a personal computer sales company knows that the price of the computers sold by the company is normally distributed with an average selling price of $1,000 and a standard deviation of $200.
a.) What is the probability that a randomly selected computer from the company inventory has a price of at least $1.100?
b.) If a customer is willing to spend between $800 and $1.100 on a computer, what is the probability that thus company can meet this need?
c.) What is the probability that a randomly selected computer from the company inventory had a price less than $900?
d.) What is the price of company computers which defines the upper 15% of their computer cots marketed to "elite" consumers?
4.) Given that z follows the standard normal distribution.
a.) P(z \geq 1.53) =
b.) P(-2.01 < z="">< 1.42)="">
c.) If the area under the standard normal curve to the left of z is 0.111, then z=
d.) What is the z value for which the area under the curve to the left of z is 0.05?
e.) What is the z value for which the area under the curve to the right of z is 0.025?
f.) P(-1 < z="" \leq="" 1)="">
5.) Seventy percent of the applications for a particular credit card are accepted. What is the probability that among the next 8 applications:
a.) none will be accepted?
b.) all will be accepted?
c.) less than 4 will be accepted?
d.) more than 3 will be accepted?
e.) What is the expected number of accepted applications among the 8?
f.) For the 8 applications, what is the variance in the number of accepted applications?