During an evolution, the minimum, maximum, and average fitness of a population is 1.2, 270, and 40, respectively. If the most fit individual is to be 3 time more likely than the average fit individual to be selected, and the least fit individual is l1/3 as likely as the average fit individual to be selected, what is the scaled fitness of an individual whose raw fitness is 58.
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- An agricultural scientist tests six types of fertilizer, labeled A, B, C, D, E, and F, to determine whether any of them produces an increase in the yield of lima beans over that obtained with the current fertilizer. For fertilizer C, the increase in yield is statistically significant at the 0.05 level. For the other five, the increase is not statistically significant. The scientist concludes that the yield obtained with fertilizer C is greater than that of the current fertilizer. Explain why this conclusion is not justified.In deciding how many customer service representatives to hire and in planning their schedules, it is important for a firm marketing electronic typewriters to study repair times for the machines. Such a study revealed that repair times have approximately an exponential distribution with a mean of 72 minutes. In planning schedules, how much time should be allowed for each repair so that the chance of any one repair time exceeding this allowed time is only 0.15?When wildebeest are more abundant, they graze the grass more heavily, so there are fewer fires and moretrees grow. Lions feed more successfully when there are more trees, so the lion population increases. Thedata on one part of this cycle, wildebeest abundance (in thousands of animals) and the percent of the grassarea that burned in the same year are on the spreadsheet. To what extent do these data support the claim that more wildebeest reduce the percent of grasslands that burn? How rapidly does burned area decrease as the number of wildebeest increases? To answer these questions, create a scatterplot and add the regression line. Describe the scatterplot. Interpret the slope and intercept in context of the problem. Does the intercept explanation make sense in the real world? Find the correlation coefficient and coefficient of determination. What do they tell us about the relationship between number of wildebeest and percent of grassland burned? Beest (in 1000s) Percent Burned…
- The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite as quickly. A cognitive psychologist is interested in whether cuttles exhibit learning (by showing a reduction in reaction time) after repeated exposure to the same environment. Initially, 10 baby cuttlefish are individually placed in a tank with a checkerboard bottom and their reaction time (time to camouflage) is recorded. Over the next month the samecuttlefish are exposed to the same environment daily and at the end of the month each cuttlefish's reaction time is recorded again. The data are recorded in the table below. Reaction Time (seconds) Subject Before After 1 58 41 2 48 45 3 54 40 4 56 42 5 55 48 6 55 41 7 43 32 8 51 44 9 62 38 10 35…A developmental psychologist experiment to determine if exposure to an enriched environment shortly after birth will cause increased brain development. Twenty, two-month-old rats are randomly selected from a pool of one thousand two-month-old rat pups. Ten of the twenty pups are exposed to an enriched environment for three weeks and the other ten to the usual environment for the same period of time. At a suitable time after the exposure, the psychologist measures the number of neurons per cm3 in each rat's brain. A comparison is then made of the mean number of neurons per cm3 for each group.a. What is the population?b. What is the independent variable?c. What is the sample?d. What is the statistics?e. What is the dependent variable?A UPS efficiency expert is interested in finding out if the years of driving experience (EXP) can be used to predict the frequency of late deliveries (LATE). Here are the data (late deliveries are per 100 ): EXP ZEXP LATE ZLATE 16 0.49 8 0.43 19 1.34 10 1.45 15 0.21 7 -0.09 15 0.21 8 0.43 14 -0.07 6 -0.60 15 0.21 8 0.43 13 -0.35 5 -1.11 12 -0.64 5 -1.11 4 -2.90 3 -2.14 15 0.21 8 0.43 16 0.49 9 0.94 17 0.78 9 0.94 MEXP = 14.25 SDEXP = 3.54 MLATE= 7.17 SDLATE = 1.95 Use α = .05 for all decisions. Determine how many late deliveries (per 100) we would predict for a driver with 20 years of experience. No explanation is required – just report the predicted value as your final answer.
- In a recent survey, ice cream truck drivers in Cincinnati, Ohio, reported they make about $280 in income on a typical summer day. The income was generally higher on days with longer work hours, particularly hot day, and on holidays. The IceCream data file includes five weeks of the driver's daily income (Income), number of hours on the road (Hours), whether it was a particularly hot day (Hot = 1 if the high temperature was above 85-degrees F, 0 otherwise), and whether it was a Holiday (Holiday = 1, 0 otherwise). 1. Predict the income of a driver working 8 hours on a hot holiday. (Round to the nearest dollar.) 2. Predict the income of a driver working 8 hours on a hot day if it was not a holiday. (Round to the nearest dollar.)At the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will vary from nest to nest. If the expected total weight of seeds gathered by a randomly chosen nest is 5 pounds, and the standarddeviationis0.5pounds,whatistheprobabilitythatthetotalcombinedweightoftheseedsgatheredby100 nests will be larger than 495 pounds by the end of next summer? To answer this question most accurately, given the information available, we would use: 1. Chebyshev’s theorem 2.Markov’s theorem (3.The Central Limit Theorem 4.The joint probability that the weight of seeds is larger than 5 pounds in each nest.If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?
- The following table is an abbreviated life expectancy table for males. current age, x 0 20 40 60 80 life expectancy, y 76.6 years 78.9 years 80.5 years 81.7 years 82.7 years a. Find the straight line that provides the best least-squares fit for these data.Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 50 clam shells in February and 27 clam shells in March. 15 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months. The point estimate for the true difference in proportion of dark growth bands between February and March is:Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 50 clam shells in February and 27 clam shells in March. 15 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months. Let ? = 0.01. A) The point estimate for the true difference in proportion of dark growth bands between February and March is:
