Suppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 3.0 seconds; what is the average value of the distribution?
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- Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births x per one thousand people in the population and the female life expectancy y (in years) are given. These data are displayed in the Figure 1 scatter plot. Also given is the product of the birthrate and the female life expectancy for each of the twelve countries. (These products, written in the column labelled "xy", may aid in calculations.) Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) xy 25.5 71.8 1830.9 18.6 73.4 1365.24 49.0 61.4 3008.6 31.0 62.4 1934.4 49.8 54.9 2734.02 45.6 59.0 2690.4 35.2 67.0 2358.4 15.5 75.8 1174.9 16.0 72.6 1161.6 40.3 65.0 2619.5 51.0 59.7 3044.7 26.2 74.1 1941.42 What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four…The population mean will always be the same as the mean of all possible X¯ that can be computed from samples of size 21.Suppose that the length of long distance phone calls, mea- sured in minutes, is known to have an exponential distribution with the average length of a call equal to 15 minutes. Find the CDF.
- A researcher believes at 49% of people who grew up as the only child have an IQ score over 100. However, unknown to the researcher this figure is actually 50% which is the same as the general population. To attempt to find evidence for the claim, the researcher is going to take a random sample of 400 people who grew up as an only child. Let X be the proportion of people in the sample with an IQ score above 100. (a) find the mean of C (b) find the standard deviation of X (c) compute the approximation for P(x >0.49) , which is the probability that there will be 49% or more with the IQ scores over 100 in the sample. Round your answer to four decimal places. * greater than sign, is supposed to be greater than or equal to sign*Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week Buildup Factor 2 3 4…Suppose the mean and standard deviation of the GPAs at Loyola are Xbar = 1.963; and s = 0.257Catherine's GPA has a z-score of 2.010. What is Catherine's GPA?
- Chebyshev's Theorem states that for any set of numbers, the fraction that will like within k Standard deviations of the mean is at least 1- 1/k2. Use this theorem to find the fraxtion of all the numbers of a data that must lie within 3 standard deviations from the mean.The manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. After checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 5 minutes. What propotion of customers require more than 10 minutes to check out?Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar.A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year 1 2 3 4 5 6 7 $ per capita 32.27 34.06 37.83 43.32 44.62 49.67 51.83 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data…
- A special education teacher did research on whether or not there is a relationship between the number of students in his class and the number incidents of “acting out” behaviors exhibited by the autistic students in the classroom. He collects data for a year and aggregates them by month. He obtained the statistics below, r= -.863 R2=.74 b= -1.212294 a= 131.176598 10.) How does the presence of more students affect the incidents in the class? a) as students are added the incidences increase b) as students are added the incidences decrease c) the number of students does not affect acting out d) the number of students caused more incidents How much of the variability of acting out is explained by the number of students in the class?___________For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is p = 1 - 7.2 where p is the minimum percentage of scores that fall within k standard deviations on both sides of the mean. Use this formula to answer the following questions. a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 2.1 standard deviations on both sides of the mean? b) If you have scores that are normally distributed, find the percentage of scores that fall within 2.1 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 96 percent of the scores? Note: To answer part c you will need to solve the equation for k.6. For a distribution of scores, X = 40 corresponds to a z-score ofz = +1.00, and X = 28 corresponds to a z-score of z =- 0.50. What are the values for the mean and standard deviation for the distribution?
