week 4 practice test

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American Public University *

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MATH302

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Statistics

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Jan 9, 2024

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docx

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Uploaded by 1500hayes

Question 1 1 / 1 point Arm span is the physical measurement of the length of an individual's arms from fingertip to fingertip. A man's arm span is approximately normally distributed with mean of 70 inches with a standard deviation of 4.5 inches. Find length in inches of the 99th percentile for a man's arm span. Round answer to 2 decimal places. Answer: ___ 80.47 ___ Question 2 1 / 1 point The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. What is the length in cm of the longest 15% of Atlantic cod in this area? Round answer to 2 decimal places. Answer: ___ 53.78 ___ Question 3 1 / 1 point Find P(Z ≥ 1.8). Round answer to 4 decimal places. Answer: ___ 0.0359 ___ Question 4 1 / 1 point Find the probability that falls in the shaded area. Shaded graph that extends from 0 to 8.5 shaded up to 5. X axis goes from 0 to 10 and y-axis is labeled with 1/8 0.5 0.625 0.125 0.438 Question 5 1 / 1 point A population has the distribution given by the following histogram with a mean of 0.6 and standard deviation of 0.2. Population chart starts at 0.0 goes to 1.0 Select the expected distribution of mean for samples of size 45 selected from the above population. sample mean distribution graph Question 6 1 / 1 point The life of an electric component has an exponential distribution with a mean of 10 years. What is the probability that a randomly selected one such component has a life more than 7 years? Answer: (Round to 4 decimal places.) ___ 0.4966 ___ Question 7 1 / 1 point

The average lifetime of a set of tires is three years. The manufacturer will replace any set of tires failing within two years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within two years of the date of purchase? 0.8647 0.2212 0.4866 0.9997 Question 8 1 / 1 point Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Find the probability that a light bulb lasts between six and ten years. 0.1175 0.1859 9.6318 0.3034 0.3682 Question 9 1 / 1 point The life of an electric component has an exponential distribution with a mean of 8 years. What is the probability that a randomly selected one such component has a life less than 5 years? Answer: (round to 4 decimal places) ___ 0.4647 ___ Question 10 1 / 1 point Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 28 and 33 miles per gallon is: Answer: (Round to two decimal place) ___ 0.50 ___ Question 11 1 / 1 point Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 5 and 17 minutes, inclusive. Let X = the time, in minutes, it takes a barber to complete a haircut. Then X ~ U (5, 17). Find the probability that a randomly selected barber needs at least seven minutes to complete the haircut, P(x > 7) (round to 4 decimal places) Answer: ___ 0.8333 ___ Question 12 1 / 1 point The waiting time for a bus has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this bus is less than 5 minutes on a given day? Answer: (Round to two decimal place.) ___ 0.50 ___ Question 13 1 / 1 point

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