(1) Consider a normal distribution with mean 38 and standarddeviation 3. What is the probability a value selected at randomfrom this distribution is greater than 38? (Round your answer totwo decimal places.)
(4) Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.) ?= 14.1; ? = 4.4 P(10 ? x ? 26)=
(5) Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.)
? = 15.0; ? = 2.8 P(8 ? x ?12) =
(6) Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.) ?= 107; ? = 11 P(x ? 120) =
(7) Assume that x has a normal distribution with thespecified mean and standard deviation. Find the indicatedprobability. (Round your answer to four decimal places.)
? = 2.1; ? = 0.39 P(x ? 2) =
(8) Find z such that 4.2% of the standard normal curvelies to the left of z. (Round your answer to two decimalplaces.)
z =
Sketch the area described.
(9)Find z such that 2.7% of the standard normal curve lies tothe right of z. (Round your answer to two decimalplaces).
z=
Sketch the area described
(10) Find the z value such that 86% of the standardnormal curve lies between ?z and z. (Round youranswer to two decimal places.)
z =
Sketch the area described.
(11) Thickness measurements of ancient prehistoric NativeAmerican pot shards discovered in a Hopi village are approximatelynormally distributed, with a mean of 5.3millimeters (mm) and astandard deviation of 0.8 mm. For a randomly found shard, find thefollowing probabilities. (Round your answers to four decimalplaces.)
(a) the thickness is less than 3.0 mm
(b) the thickness is more than 7.0 mm
(c) the thickness is between 3.0 mm and 7.0 mm
(12) Quick Start Company makes 12-volt car batteries. After manyyears of product testing, the company knows that the average lifeof a Quick Start battery is normally distributed, with a mean of45.2 months and a standard deviation of 8.1 months.
(a) If Quick Start guarantees a full refund on any battery thatfails within the 36-month period after purchase, what percentage ofits batteries will the company expect to replace? (Round youranswer to two decimal places.)
%
(b) If Quick Start does not want to make refunds for more than 11%of its batteries under the full-refund guarantee policy, for howlong should the company guarantee the batteries (to the nearestmonth)?
months
(13) How much should a healthy kitten weigh? Suppose that ahealthy 10-week-old (domestic) kitten should weigh an average of? = 25.3 ounces with a (95% of data) range from 15.0 to35.6 ounces. Let x be a random variable that representsthe weight (in ounces) of a healthy 10-week-old kitten. Assume thatx has a distribution that is approximately normal.
(a) The empirical rule (Section 7.1) indicates that for asymmetrical and bell-shaped distribution, approximately 95% of thedata lies within two standard deviations of the mean. Therefore, a95% range of data values extending from ? ? 2? to? + 2? is often used for "commonly occurring"data values. Note that the interval from ? ? 2?to ? + 2? is 4? in length. This leads toa "rule of thumb" for estimating the standard deviation from a 95%range of data values.Estimating the standarddeviation
For a symmetric, bell-shaped distribution,?
=
where it is estimated that about 95% of the commonly occurringdata values fall into this range.Estimate the standard deviation ofthe x distribution. (Round your answer to two decimalplaces.)
oz
(b) What is the probability that a healthy 10-week-old kitten willweigh less than 14 ounces? (Round your answer to four decimalplaces.)
(c) What is the probability that a healthy 10-week-old kitten willweigh more than 33 ounces? (Round your answer to four decimalplaces.)
(d) What is the probability that a healthy 10-week-old kitten willweigh between 14 and 33 ounces? (Round your answer to four decimalplaces.)
(e) A kitten whose weight is in the bottom 7% of the probabilitydistribution of weights is called undernourished. What isthe cutoff point for the weight of an undernourished kitten? (Roundyour answer to two decimal places.)
oz
(14) A relay microchip in a telecommunications satellite has alife expectancy that follows a normal distribution with a mean of93 months and a standard deviation of 3.1 months. When thiscomputer-relay microchip malfunctions, the entire satellite isuseless. A large London insurance company is going to insure thesatellite for 50 million dollars. Assume that the only part of thesatellite in question is the microchip. All other components willwork indefinitely.
(a) For how many months should the satellite be insured to be90% confident that it will last beyond the insurance date? (Roundyour answer to the nearest month.)
months
(b) If the satellite is insured for 84 months, what is theprobability that it will malfunction before the insurance coverageends? (Round your answer to four decimal places.)
(c) If the satellite is insured for 84 months, what is the expectedloss to the insurance company? (Round your answer to the nearestdollar.)
$
(d) If the insurance company charges $3 million for 84 months ofinsurance, how much profit does the company expect to make? (Roundyour answer to the nearest dollar.)
(14) The amount of money spent weekly on cleaning, maintenance,and repairs at a large restaurant was observed over a long periodof time to be approximately normally distributed, with mean? = $627 and standard deviation ? = $46.
(a) If $646 is budgeted for next week, what is the probabilitythat the actual costs will exceed the budgeted amount? (Round youranswer to four decimal places.)
(b) How much should be budgeted for weekly repairs, cleaning, andmaintenance so that the probability that the budgeted amount willbe exceeded in a given week is only 0.14? (Round your answer to thenearest dollar.)
