Question

(1) Consider a normal distribution with mean 38 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 38? (Round your answer to two decimal places.)

(4) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 14.1; σ = 4.4 P(10 ≤ x ≤ 26)=

(5) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 15.0; σ = 2.8 P(8 ≤ x ≤ 12) =

(6) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 107; σ = 11 P(x ≥ 120) =

(7) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 2.1; σ = 0.39 P(x ≥ 2) =

(8) Find z such that 4.2% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.)
z =

Sketch the area described.

(9)Find z such that 2.7% of the standard normal curve lies to the right of z. (Round your answer to two decimal places).

z=

Sketch the area described

(10) Find the z value such that 86% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)
z =

Sketch the area described.

(11) Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.3millimeters (mm) and a standard deviation of 0.8 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(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 many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45.2 months and a standard deviation of 8.1 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer 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 how long should the company guarantee the batteries (to the nearest month)?
months

(13) How much should a healthy kitten weigh? Suppose that a healthy 10-week-old (domestic) kitten should weigh an average of μ = 25.3 ounces with a (95% of data) range from 15.0 to 35.6 ounces. Let x be a random variable that represents the weight (in ounces) of a healthy 10-week-old kitten. Assume that x has a distribution that is approximately normal.

(a) The empirical rule (Section 7.1) indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values.Estimating the standard deviation

For a symmetric, bell-shaped distribution,≈

range

4

=

high value − low value

4

where it is estimated that about 95% of the commonly occurring data values fall into this range.Estimate the standard deviation of the x distribution. (Round your answer to two decimal places.)
oz

(b) What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces? (Round your answer to four decimal places.)


(c) What is the probability that a healthy 10-week-old kitten will weigh more than 33 ounces? (Round your answer to four decimal places.)


(d) What is the probability that a healthy 10-week-old kitten will weigh between 14 and 33 ounces? (Round your answer to four decimal places.)


(e) A kitten whose weight is in the bottom 7% of the probability distribution of weights is called undernourished. What is the cutoff point for the weight of an undernourished kitten? (Round your answer to two decimal places.)
oz

(14) A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 93 months and a standard deviation of 3.1 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.

(a) For how many months should the satellite be insured to be 90% confident that it will last beyond the insurance date? (Round your answer to the nearest month.)
months

(b) If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (Round your answer to four decimal places.)


(c) If the satellite is insured for 84 months, what is the expected loss to the insurance company? (Round your answer to the nearest dollar.)
$  

(d) If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make? (Round your 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 period of time to be approximately normally distributed, with mean μ = $627 and standard deviation σ = $46.

(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)


(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.14? (Round your answer to the nearest dollar.)

Answer 1