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# Standard deviations and mean

by | Aug 17, 2021 | Assignment

Within 2.49 standard deviations of the mean.  less than ??1.5?4 Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including the number xx of hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.99  hours of sleep, with a standard deviation of 1.38  hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.(a) P(x?6.4)= What is the probability that a visually impaired student gets less than 6.4 hours of sleep?P(6?x?9.75)=answer =  hours Fourty percent of students get less than how many hours of sleep on a typical day?6 Suppose xx is a normally distributed random variable with ?=8.8 and ?=3.7. Find each of the following probabilities:(a) P(10.7?x?14.1)=(b) P(10?x?15.5)=(c) P(5.5?x?14)=(d) P(x?11.3)=P(x?14.5)= 7Find the following probabilities for the standard normal random variable zz: (a) P(?0.53?z?0.51)=(b) P(?0.77?z?0.97)=(c) P(z?1.47)=(d) P(z>?0.43)=8 A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 45 miles and a standard deviation of 7 miles. Find the probability of the following events:A. The car travels more than 51 miles per gallon.Probability =  B. The car travels less than 41 miles per gallon.Probability =  C. The car travels between 37 and 50 miles per gallon.Probability =  9College students average 7.8 hours of sleep per night with a standard deviation of 45 minutes. If the amount of sleep is normally distributed, what is the probability a college student sleeps for more than 8.7 hours on a given day?Probability = 10 The lifetime of lightbulbs that are advertised to last for 3700 hours are normally distributed with a mean of 4000 hours and a standard deviation of 200 hours. What is the probability that a bulb lasts longer than the advertised figure?Probability = 11Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank’s Visa cardholders reveals that the amount is normally distributed with a mean of 27 dollars and a standard deviation of 7 dollars.A. What proportion of the bank’s Visa cardholders pay more than 31 dollars in interest?Proportion = B. What proportion of the bank’s Visa cardholders pay more than 38 dollars in interest?Proportion = C. What proportion of the bank’s Visa cardholders pay less than 17 dollars in interest?Proportion = D. What interest payment is exceeded by only 19% of the bank’s Visa cardholders?Interest Payment = 12The top-selling Red and Voss tire is rated 70000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 84000 miles and a standard deviation of 7000 miles.A. What is the probability that the tire wears out before 70000 miles?Probability = B. What is the probability that a tire lasts more than 89000 miles?Probability = 13(1 point) Find the z-score such that:(a) The area under the standard normal curve to its left is 0.5017 z = (b) The area under the standard normal curve to its left is 0.668 z = (c) The area under the standard normal curve to its right is 0.1038 z = (d) The area under the standard normal curve to its right is 0.2013 z =

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