Stats Work 2

1. The maximum patent life for a new drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug—that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below:

1. What is the value of “?” so that the above is the probability distribution?

• Find the mean and standard deviation of patent life for a new drug.

• What is the probability of a patent living at least ten years for new drugs?

• If the patent lives at least eleven years for new drugs, is this unusual or usual? Show your work.

• Show your work whether the given probability distribution is a binomial probability distribution or not.

• A multiple-choice examination has 20 questions, each with four possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess.
• What is the probability that he answers exactly ten questions correctly?

• What is the probability that he answers at least twelve questions correctly?

• Find the mean and standard deviation of the students answer the questions correctly.

• Is it unusual if the student answers eleven questions correctly? Show your work.

• The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes.
• Find the probability distribution function f(x). Define the random variable x is a continuous random variable or discrete random variable.

• What is the probability that the cycle time exceeds 65 minutes?

• Wires manufactured for use in a computer system are specified to have resistances between

.12 and .14 ohms. The actual measured resistances of the wires produced by company A have an unknown distribution with mean .13 ohm and standard deviation .05 ohm.

1. Find a probability if randomly selected a resistance has at least 0.13 ohm, if possible.

• If 40 resistances are randomly selected find the probability that their average measurement value is between 0.12 to 0.14 ohm, if possible.

• Based on the study at Indiana University, it is known that 11 % of population have green eyes. If you randomly choose 560 people,
• Check the conditions or requirements to use Normal Distribution.

• Compute probability that greater than 70 people have green eyes.

• Would it be unusual if less than 50 people have green eyes, show your work.

• The bank of American issues Visa and MasterCard credit cards. It is known that the balances on all cards issued by BOA have a mean of $756 and a standard deviation of $210. Assume the balances on those cards are normally distributed.
• Find the probability that randomly selected credit card issues by BOA have a balance over

$1000.

• Find the probability that the average of 20 selected credit cards issued by BOA has a balance over $1000.

• BOA is planning to send free gifts to the top 10% of card holders with high balance. What is the cut-off balance for free gift?