cKathryn Bollinger and Benjamin Aurispa, November 28, 2011 1Week-In-Review #10 (8.5, 8.6, 5.1)1. Let Z be the standard normal random variable. Calculate the following probabilities:(a) P (−2 ≤ Z < 0.22)(b) P (Z ≤ 1.75)(c) P (Z > −0.35)2. Let Z be the standard normal random variable. Find a such that(a) P (Z < a) = 0.8158(b) P (Z > a) = 0.3257(c) P (−a < Z < a) = 0.6102cKathryn Bollinger and Benjamin Aurispa, November 28, 2011 23. Let X be a normal random variable with µ = 260 and σ = 35. Find each of the following.(a) P (X < 200)(b) P (X ≥ 180)(c) The value of a such that P (260 < X < a) = 0.22(d) The values of a and b such that P (a < X < b) = 0.4198 if a and b are symmetric about the mean.cKathryn Bollinger and Benjamin Aurispa, November 28, 2011 34. Sup pose weights of bags of snack mix are normally distributed with a mean of 10 ounces and a standarddeviation of 0.6 ounces. What is the probability that a bag selected at r an dom weighs(a) Between 9.5 and 11 ounces?(b) At least 9 ounces?(c) Less than 8.5 ounces?5. A study finds that the lifespan of phone b atteries are normally d istributed with a mean of 2 years and astandard deviation of 1.5 months.(a) What is the probability that a phone battery will have a lifespan between 22 and 26 months?(b) What battery lifespan corr esponds to the 95thpercentile?cKathryn Bollinger and Benjamin Aurispa, November 28, 2011 46. Find the amount of money at the end of 5 years on a $200 deposit in an account paying simple interest ata rate of 4.75% per year. How much interest is earned?7. A bank deposit paying simple interest grew from an initial sum of $2000 to a sum of $2150 in 7 months.Find the interest rate.8. How much money will be in an account after 2 years on a $500 deposit that earns interest at a rate of 5%per year compounded continuously?9. If Mark invests $5000 into an account paying interest at a r ate of 8% per year compounded m onthly, howmuch money will he have at the end of 5 years (assuming n o add itional deposits or withdrawals)?cKathryn Bollinger and Benjamin Aurispa, November 28, 2011 510. In 18 months Brian needs $1750 in order to buy a specific computer. If he finds an account paying interestat a rate of 5.95% per year compounded weekly, how much could he invest now in order to have the moneyhe n eeds for the computer?11. Kevin inherits $50,000. If he invests it by placing it into an account paying interest at a rate of 10.5%per year compounded monthly, how long would he have to leave his money in the account before having$100,000?12. What interest rate, compounded daily, will quadruple $1200 after 5 years?13. A major credit card company has a finance charge of 1.5% per month on the outstand ing indebtedness.Susie charged $1000 and did not pay her bill for 6 months. What is the bill after the 6 months?cKathryn Bollinger and Benjamin Aurispa, November 28, 2011 614. Which account would be a better account for an investment? For a credit card?OPTION A: 9% per year, compounded monthlyOPTION B: 8.8% per year, compound ed d ailyOPTION C: 8.9% per year, compounded continuously15. Determine whether the following s tatements are True or False.(a) A normal curve with a higher variance is taller than one with a lower variance.(b) In a normal distribution, approximately 99.73% of the data lies fur ther than 3 standard deviations fromthe mean.(c) A normal random variable with a mean of zero is the standard normal curve.(d) The m ore times a year an account is compounded, the more interest that is
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