Mr. Orchard s Math 141 WIR 8.5, 8.6, 5.1 Week 13

Transcription

1 1. Find the following probabilities, where Z is a random variable with a standard normal distribution and X is a normal random variable with mean µ = 380 and standard deviation σ = 21: (Round your answers to four decimal places.) (a) P ( 1 Z 1) (b) P (X < 419) (c) P (390 X < 414) (d) P (Z 0.61) (e) P (X = 380)

2 2. Let Z be the standard normal random variable. Find the values of a that satisfy the given probabilities: (Round your answer to four decimal places.) (a) P (Z < a) = (b) P (Z a) = (c) P ( a < Z < a) = Let X be a normal random variable with a mean of 80 and a standard deviation of 4. Find the values of A and B such that P (A X < B) = if A and B are symmetric about the mean. (Round to four decimal places.)

3 4. The number of chocolate chips in certain brand s bags are normally distributed with a mean of 291 chips and a standard deviation of 18 chips. (a) What is the minimum number of chocolate chips needed in bag to have a bag in the top 1% of number of chocolate chips? (Round to the nearest chocolate chip.) (b) What is the probability that a bag has more than 300 chocolate chips? (Round to four decimal places.) (c) What is the probability that a bag has more than 250, but less than or equal to 490 chocolate chips? (Round to four decimal places.) 5. A company manufactures electric light bulbs. Labratory tests show that the lives of the bulbs are normally distributed with a mean of 800 hours and a variance of hours 2. What is the probability that one of these light bulbs selected at random will burn for the following times? (Round to four decimal places.) (a) between 800 and 950 hours (b) more than 950 hours (c) between 650 and 850 hours

4 6. One way to curve a test is to give the top 15% of the class an A, the next 25% a B, the next 30% a C, the next 20% a D, and the bottom 10% an F. If the grades are normally distributed with a mean of 64 and a standard deviation of 15, find the point cut off for each letter grade. (Round your answers to two decimal places.) 7. Find the accumulated amount at the end of 15 months on a $1800 bank deposit paying simple interest at a rate of 7% per year. Round your answer to the nearest cent. 8. Determine the simple interest rate at which $1200 will grow to $1252 in 8 months. Round your answer to one decimal place. 9. Four and a half years ago, Chris invested $10,000 in a retirement fund that grew at a rate of 11.14% per year compounded quarterly. What is her account worth now? Round your answer to the nearest cent.

5 10. A young man is the beneficiary of a trust fund established for him 25 years ago. If the original amount placed in the trust was $40,000, and it grew at 10% per year, how much money has the account earned in interest if the account is compounded (round your answers to the nearest cent) (a) annually? (b) quarterly? (c) monthly? (d) continuously? 11. Bank A offers a bank account compounded quarterly at a nominal rate of 4.9% per year. Bank B offers an account compounded continuously at a rate of 4.8% per year. Determine which account is better for your money by comparing effective rates of interest.

6 12. Bank A offers a loan compounded twice a year at a nominal rate of 10.5% per year. Bank B offers a loan at a yearly rate of 10.3% compounded monthly. Determine which loan is the better offer by comparing effective rates of interest. 13. A bank account with an interest rate of 10% per year compounded continuously currently has $15,000 in it. (a) How much was put into the account when it was opened 10 years ago? Round your asnwer to the nearest cent. (b) What is the effective rate of interest of this account? Round your answer to two decimal places.