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 Magnetic Susceptibility Number of Readings Estimated Probability "cool" 0 ≤ x < 10 24 24/120 = 0.20 "neutral" 10 ≤ x < 20 60 60/120 = 0.50 "warm" 20 ≤ x < 30 24 24/120 = 0.20 "very interesting" 30 ≤ x < 40 6 6/120 = 0.05 "hot spot" 40 ≤ x 6 6/120 = 0.05Suppose a 'hot spot' is a site with a reading of 40 or higher.   A. In a binomial setting, let us call success a 'hot spot'. Use the table to find p= P(success) = p(40≤ x) for a single trial.    B. Suppose you decide to take readings at random until you find your first 'hotspot'. Let n be a random variable representing the trial on which you get your first 'hot spot'. Use the geometric probability distribution to write out a formula for P(n).    C. What is the probability that you will need more than six readings to find the first 'hot spot'? Compute P(n>6). (round to three decimal places)

Question 4 The ten year extreme wave height (H) at a site of interest for offshore drilling and extraction can be assumed to floow Rayleigh distribution with a mean wave height of 16 ft. ( mean wave height = 2.5 x o). Determine the following: • Probability of a wave height greater than 24 feet. • Probability of a wave height less than or equal to 18 feet. • Probability of seeing a wave less than or equal to 24 feet, but greater than 18 feet. • What is the one in 50000 wave height? (i.e. the wave height that has a probability of 0.002% of being exceeded.)

Question 8 The volume of a hand sanitizer filled into a container is contimuous uniformly distributed between 274 and 290 millimeters. What are the mean and variance of the volume of hand sanitizer? 228 and 36.67 None 282 and 36.67 282 and 21.33

QUESTION 10 Solve the problem. Find the standardized test statistic t for a sample with n = 12, x = 20.6, s = 2.1, and a = 0.01 if Ha: H 21.1. Round your answer to three decimal places. O a. -0.825 O b. -0.037 OC. -0.381 O d.-0.008

Question 6

The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site. Raw Material Regional Percent of Stone Tools Observed Number of Tools as Current excavation Site Basalt 61.3% 893 Obsidian 10.6% 165 Welded Tuff 11.4% 179 Pedernal chert 13.1% 198 Other 3.6% 51 (A) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Question 5 The average amount of time boys and girls of ages 7 through 11 spend playing sports each day is believed to be the same. An experiment is done and data is collected, resulting in the table below. Assume that the populations follow a normal distribution with equal variances. Is there a difference in the mean amount of time boys and girls spend playing sports each day? Test at 5% level of significance. Girl Boys Sample size Average number of hours playing Sample standard deviation sports per day 2 hours 0.75 3.2 hours 9 16

QUESTION 20 The time spent on social media platforms per day by adults has a distribution with a mean of 125 minutes and a standard deviation of 16 minutes. A random sample of size 16 adults is selected from the population. Find the mean and standard error of the sample mean time spent on social media platforms per day.

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