A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 173.4-cm and a standard deviation of 1.1-cm. For shipment, 23 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 172.8-cm. P(M < 172.8-cm) =

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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.3 years, and standard deviation of 0.6 years. If 15 items are picked at random, 5% of the time their mean life will be less than how many years? Give your answer to one decimal place.

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A particular fruit's weights are normally distributed, with a mean of 553 grams and a standard deviation of 16 grams. If you pick 35 fruits at random, then 2% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

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The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4917 households discard waste with weights having a mean that exceeds 26.97 lb/wk. For many different weeks, it is found that the samples of 4917 households have weights that are normally distributed with a mean of 26.73 lb and a standard deviation of 12.68 lb. What is the proportion of weeks in which the waste disposal facility is overloaded? P(M > 26.97) = Enter your answer as a number accurate to 4 decimal places.

Is this an acceptable level, or should action be taken to correct a problem of an overloaded system?

• No, this is not an acceptable level because it is not unusual for the system to be overloaded.
• Yes, this is an acceptable level because it is unusual for the system to be overloaded.

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A population of values has a normal distribution with =157.5 and =70.8. You intend to draw a random sample of size n=203. Find P₄₄, which is the mean separating the bottom 44% means from the top 56% means. P₄₄ (for sample means) =

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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years. He then randomly selects records on 47 laptops sold in the past and finds that the mean replacement time is 3.6 years. Assuming that the laptop replacement times have a mean of 3.8 years and a standard deviation of 0.4 years, find the probability that 47 randomly selected laptops will have a mean replacement time of 3.6 years or less. P(M < 3.6 years) = Enter your answer as a number accurate to 4 decimal places. Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone

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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.953 g and a standard deviation of 0.328 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 50 cigarettes with a mean nicotine amount of 0.907 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 50 cigarettes with a mean of 0.907 g or less. P(M < 0.907 g) = Enter your answer as a number accurate to 4 decimal places. Based on the result above, is it valid to claim that the amount of nicotine is lower?

• Yes. The probability of this data is unlikely to have occurred by chance alone.
• No. The probability of obtaining this data is high enough to have been a chance occurrence.

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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 166.1-cm and a standard deviation of 0.7-cm. For shipment, 18 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 165.7-cm and 166.4-cm. P(165.7-cm < M < 166.4-cm) = Enter your answer as a number accurate to 4 decimal places.

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A population of values has a normal distribution with =119=119 and =72.2=72.2. You intend to draw a random sample of size n=51n=51. Find P₁₉, which is the score separating the bottom 19% scores from the top 81% scores. P₁₉ (for single values) = Find P₁₉, which is the mean separating the bottom 19% means from the top 81% means. P₁₉ (for sample means) = Enter your answers as numbers accurate to 1 decimal place.

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Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 138000 dollars. Assume the standard deviation is 30000 dollars. Suppose you take a simple random sample of 72 graduates. Find the probability that a single randomly selected salary exceeds 135000 dollars. P(X > 135000) = Find the probability that a sample of size n=72n=72 is randomly selected with a mean that exceeds 135000 dollars. P(M > 135000) = Enter your answers as numbers accurate to 4 decimal places.

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A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 38 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 38 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 30 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is less than 39. P(X < 39) = Find the probability that a sample of size n=30n=30 is randomly selected with a mean less than 39. P(M < 39) = Enter your answers as numbers accurate to 4 decimal places.

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CNNBC recently reported that the mean annual cost of auto insurance is 963 dollars. Assume the standard deviation is 280 dollars. You take a simple random sample of 80 auto insurance policies. Find the probability that a single randomly selected value is less than 977 dollars. P(X < 977) = Find the probability that a sample of size n=80n=80 is randomly selected with a mean less than 977 dollars. P(M < 977) = Enter your answers as numbers accurate to 4 decimal places.

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CNNBC recently reported that the mean annual cost of auto insurance is 1031 dollars. Assume the standard deviation is 232 dollars. You take a simple random sample of 64 auto insurance policies. Find the probability that a single randomly selected value exceeds 998 dollars. P(X > 998) = Find the probability that a sample of size n=64n=64 is randomly selected with a mean that exceeds 998 dollars. P(M > 998) = Enter your answers as numbers accurate to 4 decimal places.

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Scores for a common standardized college aptitude test are normally distributed with a mean of 494 and a standard deviation of 107. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 544.4. P(X > 544.4) = Enter your answer as a number accurate to 4 decimal places. If 13 of the men are randomly selected, find the probability that their mean score is at least 544.4. P(M > 544.4) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 13 men does result in a mean score of 544.4, is there strong evidence to support the claim that the course is actually effective?

• Yes. The probability indicates that is is unlikely that by chance, a randomly selected group of students would get a mean as high as 544.4.
• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 544.4.

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The lengths of pregnancies in a small rural village are normally distributed with a mean of 264 days and a standard deviation of 16 days. A distribution of values is normal with a mean of 264 and a standard deviation of 16. What percentage of pregnancies last fewer than 310 days? P(X < 310 days) = % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).

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A population of values has a normal distribution with =94.9=94.9 and =86.6=86.6. You intend to draw a random sample of size n=70n=70. Find the probability that a sample of size n=70n=70 is randomly selected with a mean greater than 71.1. P(M > 71.1) = Enter your answers as numbers accurate to 4 decimal places.

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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 132.4-cm and a standard deviation of 2.3-cm. Find the probability that the length of a randomly selected steel rod is less than 132.6-cm. P(X < 132.6-cm) = Enter your answer as a number accurate to 4 decimal places.

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Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 100.5 ft and a standard deviation of 5.3 ft. A tree of this type grows in my backyard, and it stands 88.8 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. P(X<88.8) = Enter your answer accurate to 4 decimal places.

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A population of values has a normal distribution with =26.6 and =83. You intend to draw a random sample of size n=178. Find the probability that a sample of size n=178 is randomly selected with a mean between 7.9 and 46.5. P(7.9 < M < 46.5) = Enter your answers as numbers accurate to 4 decimal places.

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On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 424 pounds and a standard deviation of 39 pounds. The cow transport truck holds 9 cows and can hold a maximum weight of 4104. If 9 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 4104? (This is the same as asking what is the probability that their mean weight is over 456.) P(M>456)= Give answer correct to four decimal places.

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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 222.8-cm and a standard deviation of 0.9-cm. Find the probability that the length of a randomly selected steel rod is between 220.1-cm and 224.3-cm. P(220.1

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The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 61.5 with a standard deviation of 9. Assume that the distribution is approximately normal. Find the probability that an elite athlete has a maximum oxygen uptake of at most 46.2 ml/kg. (Round answer to four decimal places.)

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The population of weights for men attending a local health club is normally distributed with a mean of 171-lbs and a standard deviation of 27-lbs. An elevator in the health club is limited to 32 occupants, but it will be overloaded if the total weight is in excess of 5952-lbs. Assume that there are 32 men in the elevator. What is the average weight of the 32 men beyond which the elevator would be considered overloaded? average weight = lbs What is the probability that one randomly selected male health club member will exceed this weight? P(one man exceeds) = (Report answer accurate to 4 decimal places.) If we assume that 32 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded? P(elevator overloaded) = (Report answer accurate to 4 decimal places.) If the elevator is full (on average) 4 times a day, how many times will the elevator be overloaded in one (non-leap) year? number of times overloaded = (Report answer rounded to the nearest whole number.)