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Assignment # 7Name:Full credit12Section:Extra credit2Show all your work to get credit!Total possible14Points achieved:241/19The average amount of precipitation in Dallas, Texas, during the month of April is 3.5 inches (The World Almanac, 2000). Assume that a normal distribution applies and that the standard deviation is .8 inches.What percentage of the time does the amount of rainfall in April exceed 5 inches? (1 point)Px>5=Pz>5-3.50.8=Pz>1.875=0.0304Therefore it exceeds 5 inches approximately 3.04% of the time.What percentage of the time is the amount of rainfall in April less than 3 inches? (1 point)Px<3=Pz<3-3.50.8=Pz<-0.625=0.2660Therefore it is less than 3 inches 26.6% of the time.A month is classified as extremely wet if the amount of rainfall is in the upper 10% for that month. How much precipitation must fall in April for it to be classified as extremely wet? (1 point)x=zσ+μ=1.28160.8+3.5=4.52Therefore 4.52 inches of precipitation must fall for it to be classified as extremely wet.241/21A person must score in the upper 2% of the population on an IQ test to qualify for a membership in Mensa, the international high-IQ society (U.S. Airways Attaché, September 2000). If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa? (1 point)x=zσ+μ=2.053715+100=130.8Therefore a person must score at least 130.8 in order to qualify for Mensa.242/23The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.What is the probability of completing the exam in one hour or less? (1 point)Px<60=Pz<60-8010=Pz<-2=0.02275What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (1 point)P60<x<75=P60-8010<z<75-8010=P-2<x<-0.5=0.2857Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time? (1 point)Px>90=Pz>90-8010=Pz>1=0.1587Number of students who will be unable to complete: 0.158760=9.52?10 students.276/18A population has a mean of 200 and a standard deviation of 50. A simple random sample of size 100 will be taken and the sample mean x will be used to estimate the population mean.What is the expected value of x? (0.5 points)Ex=μx=200What is the standard deviation of x? (0.5 points)σx=σn=5010=5Show the sampling distribution of x. (1 point)x ~ N(200,5)What does the sampling distribution of x show? (1 point)Probability distribution of x.277/19A population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and x is used to estimate μ.What is the probability that the sample mean will be within ±5 of the population mean? (1 point)P195<x<205=P195-2005<z<205-2005=P-1<z<1=0.6827277/20Assume the population standard deviation is σ = 25. Compute the standard error of the mean, σx, for sample sizes of 50. (0.5 points)σx=2550=3.536Compute the standard error of the mean, σx, for sample sizes of 100. (0.5 points)σx=25100=2.5Compute the standard error of the mean, σx, for sample sizes of 150. (0.5 points)σx=25150=2.041Compute the standard error of the mean, σx, for sample sizes of 200. (0.5 points)σx=25200=1.768What can you say about the size of the standard error of the mean as the sample size is increased? (1 point)As the sample size increases, the size of the standard error of the mean reduces. ................
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