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, (cmg x 10-6) Number of centimeter-gram-second × 10-6 Magnetic Susceptibility 0 < x < 10 10 < x < 20 20 < x < 30 30 < x < 40 Estimated Readings 24 Comment Probability 24/120 = 0.20 60/120 18/120 12/120 6/120 : "cool" "neutral" 60 0.50 "warm" = 0.15 = 0.10 = 0.05 18 "very interesting" "hot spot" 12 6. 40 < x For a site chosen at random, estimate the following probabilities. (a) P(0 < x < 30) (b) P(10 < x < 40) (c) P(x < 20) (d) P(x 2 20) (e) P(30 < x) (f) P(x not less than 10) (g) P(0 < x < 10 or 40 < x) (h) P(40 < x and 20 < x)

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Question 4. a. On a random day, a store can sell a mean value of 32 pasta packages and a standard deviation of 4. What is the probability that the total number of pasta packages sold by the store for a random sample of 58 days is less than 1862? Explain. Let b. X₁, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means M₁ = 0.8, M₂ = 2.6, μ3 = 8.4, µ4 = 2.3 pounds and variances . Find o² = 0² = 0} = 0} = 1 P(3X₁ + 1X2 + 1X3 + 2X4 ≤ 16.8)