# Assignment: IQ is normally distributed, mean of 100 and a standard deviation of 15

## Assignment: IQ is normally distributed, mean of 100 and a standard deviation of 15

Assignment: IQ is normally distributed, mean of 100 and a standard deviation of 15 Assignment: IQ is normally distributed, mean of 100 and a standard deviation of 15 Permalink: https://nursingpaperessays.com/ assignment-iq-is -deviation-of-15 / ? A) IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. 1) Give the distribution of X . X ~ __ ( __, __) 2) Find the probability that the person has an IQ greater than 115. 3) Write the probability statement: P (____) 4) What is the probability? (Round your answer to four decimal places.) 5) Sketch the graph. 6) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization. 7) Write the probability statement: P(X > x) = ____ 8) What is the minimum IQ? (Round your answer to the nearest whole number.) x =__ 9) sketch the graph. 10) The middle 60% of IQs fall between what two values? 11) Write the probability statement: P(x 1 < X < x 2 ) =___ 12) State the two values. (Round your answers to the nearest whole number.) x 1 =__ x 2 =__ Permalink: https://ulcius.com/ assignment-iq-is -deviation-of-15 / ? 13) Sketch the graph. B) Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 200 feet and a standard deviation of 44 feet. Let X = distance in feet for a fly ball. 1) Give the distribution of X ; X ~__ (__,__) 2) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 180 feet? (Round your answer to four decimal places.) 3) Sketch the graph 4) Find the 80th percentile of the distribution of fly balls in feet. (Round your answer to one decimal place.) 5) Sketch the graph. Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.) P(X < k) =___ C) Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.8 hours and the amount of time spent alone is normally distributed. We randomly survey one 4-year-old living in a rural area. We are interested in the amount of time the child spends alone per day. 1) In words, define the random variable X . a) the number of 4-year-old children that live in rural areas b) the number of people that live in rural areas c) the time (in hours) a child spends unsupervised per day d) the time (in hours) a 4-year-old spends unsupervised per week e) the time (in hours) a 4-year-old spends unsupervised per day 2) Give the distribution of X : X ~__ (__,__) 3) Find the probability that the child spends less than 1 hour per day unsupervised. 4) Write the probability statement: P (___) 5) What is the probability? (Round your answer to four decimal places.) 6) Sketch the graph. 7) What percent of the children spend over 10 hours per day unsupervised? (Round your answer to four decimal places.) 8) 60% of the children spend at least how long per day unsupervised (in hours)? (Round your answer to two decimal places.) D) Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. 1) In words, define the random variable X . a) the time (in seconds) per race b) the distance (in miles) of each lap c) the time (in seconds) per lap d) the distance (in miles) of each race 2) Give the distribution of X : X ~__ (__,__) 3) Find the percent of her laps that are completed in less than 133 seconds. (Round your answer to two decimal places.) 4) The fastest 4% of her laps are under how many seconds? (Round your answer to two decimal places.) 5) The fastest 4% of her laps are under how many seconds? (Round your answer to two decimal places.) The middle 75% of her lap times are from __ seconds to __ seconds. E) The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.5 days and a standard deviation of 1.9 days. 1) What is the median recovery time in days? F) The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4.9 days and a standard deviation of 3.4 days. 1) What is the z -score for a patient who takes 7 days to recover? (Round your answer to two decimal places.) z =__ G) The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.8 days and a standard deviation of 2.2 days. 1) What is the probability of spending more than 3 days in recovery? (Round your answer to four decimal places.) F) The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.8 days and a standard deviation of 2.3 days. What is the 75th percentile for recovery times (in days)? (Round your answer to two decimal places.) 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