A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.98 bacteria colonies per field. Let r be a random variable that represents the number of

Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below.     Magnetic Susceptibility Readings,centimeter-gram-second ✕ 10−6 (cmg ✕ 10−6) Comment MagneticSusceptibility Number ofReadings EstimatedProbability "cool" 0 ≤ x < 10 36 36/120 = 0.30 "neutral" 10 ≤ x < 20 48 48/120 = 0.40 "warm" 20 ≤ x < 30 12 12/120 = 0.10 "very interesting" 30 ≤ x < 40 18 18/120 = 0.15 "hot spot" 40 ≤ x 6 6/120 = 0.05 Do the probabilities shown in the table add up to 1? Do the probabilities need to total to 1 a. Yes, they do add to 1. The probabilities must total to…

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds):  3.06 4.97 5.01 4.13 5.02 2.91 3.88 2.55 2.91 5.18 3.68 4.54 2.65 4.14 5.11 3.19 Use a calculator to verify that the sample variance for this plot is s^2=0.923. Another random sample of years for a second plot gave the following annual wheat production (in pounds):  3.61 3.50 3.81 3.89 3.84 3.50 3.53 3.62 3.67 4.05 3.82 4.12 3.75 3.92 4.05 4.01 Use a calculator to verify that the sample variance for this plot is s^2=0.042. Suppose that we test the claim using a=0.01 that the population variance of annual wheat production for the…

Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below.

A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.80 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information. 2 3 4 5 or more 13 18 28 16 17 8 (a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below. P(r) = r! Here 1 = 2.80 is the average number of bacteria colonies per field. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.) P(0) = P(1) = Р(2) Р(3) 3 P(4) = %3D P(5 or more) = (b) Compute the expected number of colonies E = 100P(r)…