# STATS MULTIPLE PROBLEMS

1. A professor investigated the fieldwork methods used by qualitative sociologists. Searching for all published journal articled, dissertations, and conference proceedings over the previous seven years, she discovered that fieldwork methods could be categorized. Use the data table to complete parts a through c. Fieldwork Method Number of Papers Interview (I) 24 Observation + Participation (OP) 29 Observation Only (O) 15 Grounded Theory (G) 10 Total 78

a. Find the relative frequency of the number of papers for each fieldwork method category Fieldwork Method ------- Interview (I) - -------- Observation + Participation (OP) -------------- Observation Only (O)________ Grounded Theory (G)________ (Round to the nearest thousandth as needed)

2. A magazine published a study on the ammonia levels near the exit ramp of a highway tunnel. The date in the teble represents daily ammonia concentrations (in parts per million) on eight random selected days during thr afternoon drive time. Complete part a through c: 1.51 1.48 1.37 1.49 1.63 1.43 1.42 1.45

a. Find the range of the ammonia levels. Give the units of measurements for the range The range is ---------- ppm or ppm squared ( type an integer or a decimal)

b. find the variance of the ammonia levels. If possible give units of measurement for the variance The variance is _____ with ____ units of ppm squared or ppm (round to four decimal places as needed)

c. Find the standard deviation of the ammonia levels. Give the units of measurement for the standard deviation The standard deviation is ___________ ppm or ppm squared (round to three decimal places as needed)

3. If x is binomial random variable, compute p(x) for each of the cases below.

a. N=5, x=1, p=0.3; b. N=4, x=2, q=0.2; c. N=3, x=0, p=0.7; d. N=5, x=3, p=0.4; e. N=4, x=2, q=0.8; f. N=3, x=1, p=0.9. a. p(x) = ---- (Round to four decimal places as needed)

b. p(x) = ---- (Round to four decimal places as needed)

c. p(x) = ---- (Round to four decimal places as needed)

d. p(x) = ---- (Round to four decimal places as needed)

e. p(x) = ---- (Round to four decimal places as needed)

f. p(x) = ---- (Round to four decimal places as needed)

4. A national standard requires that public bridges over 20 feet in length must be inspected and rated every 2 years. The rating scale ranges from 0 (poorest rating) to 9 (highest rating). A group of engineers used a probabilistic model to forecast the inspection ratings of all major bridges in a city. For the year 2020, the engineers forecast that 5% of all major bridges in that city will have ratings of 4 or below. Complete parts a and b.

a. Use the forecast to find the probability that in a random sample of 9 major bridges in the city at least 3 will have an inspection rating of 4 or below in 2020 P(x > 3) = ---- (round to five decimal places as needed)

5. Find a value of a standard normal random variable Z, A. P(Z > 1.70) B. P(Z< -1.42) C. P(0.39 < Z < 2.63) d. P(-2.46 < Z < 1.68) (Round to three decimal places as needed)

6.) Find a value of the standard normal random variable Z, Call it Z0 (z subzero), such that the following probabilities are satisfied a. P(Z ≤ Z0) = 0.7286 b. P(- Z0 ≤ Z ≤ Z0) = 0.8358 c. P(- Z0 ≤ Z ≤ 0) = 0.4568 d. P(- 1 < Z < Z0) = 0.6097 a. Z0 = _____ b. Z0 = _____ c. Z0 = _____ d. Z0 = _____ (Round to two decimal places as needed) Please note the 0s beside the Zs are subzero,

7.) Financial analysts who make forecasts of stock prices are categorized as either "buy-side" analysts or "sell side" analysts. The mean and standard deviation of the forecast errors for both types of analysts are shown in the table to the right. Assume that the distribution of forecast errors are approx normally distributed: Buy Side Sell side Mean 0.87 -0.06 Standard Deviation 1.94 0.81 a. Find the probability that a buy side analyst has a forecast error of +2.00 or higher b. Find the probability that a sell side analyst has a forecast error of +2.00 or higher View the table of areas under the table of standardized normal curve below a. The probability that a buy side analyst has a forecast error of +2.00 or higher is _____. (Round to three decimal places as needed) b. The probability that a sell side analyst has a forecast error of +2.00 or higher is _____.(Round to three decimal places as needed) Standard Normal Distribution. table is used Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753

8. The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.5 miles per gallon.

a.What is the probability that a randomly selected hybrid gets more than 60 mpg?

b. What is the probability that a randomly selected hybrid gets 53 mpg or less?

c. What is the probability that a randomly selected hybrid gets between 58 and 61 mpg?

d. What is the probability that a randomly selected hybrid gets less than 46 miles per gallon?

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