ou measure an object's height many times and find a height of 2.05 cm and a 2σ-uncertainty of 0.03 cm. The probability that the objects true height falls beween 2.02 and 2.08 cm is     37%     45%     68.2%     95.4%     99.0%     99.7%     100%

Find the probability of the indicated event if P(E) = 0.25 and P(F) = 0.35. Find P(E or F) if P(E and F)= 0.20. P(E or F) =| (Simplify your answer.)

For each probability and percentile problem, draw the picture.The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement. In a room of 1,000 people over age 79, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.) people

d. Find​ E(x) and practically interpret this value.   Age (years) to Buy 1st Smart Speaker    Probability3    0.024    0.025    0.016    0.017    0.028    0.049    0.0410    0.0911    0.0712    0.0713    0.0714    0.0615    0.0416    0.1517    0.1418    0.15

D. 286/973; 0.294

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. (a) Find the z-score corresponding to 43 percent of fat calories, rounded to 3 decimal places. (b) Find the probability that the percent of fat calories a person consumes is more than 43. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z- score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value Click and drag the arrows to adjust the values. -3 -- 3. -1.5 (d) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 decimal places. (e) Sketch the graph and write the probability statement. 2.

X P(x) 0.2 1 0.3 2 0.05 3 0.45 Find the mean of this probability distribution. Round your answer to one decimal place.

Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $60,500. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57,500? Assume o = $6,100. %3D The probability that the mean salary of the sample is less than $57,500 is (Round to four decimal places as needed.)

Verify whether the given table represents a probability distribution.  In those cases where a probability distribution is described, find the mean and standard deviation. NOTE: The Rounding Rule for the mean and standard deviation: They should be rounded to one more decimal place than occurs in the raw data. For a group of four students, the number y who takes the Calculus II class next semester is given by this table. y           P(y) 0           0.5131 1            0.3139 2           0.0624 3           0.1102 4           0.2002 Probability distribution with μ=0.4 and σ=0.4 Probability distribution with μ=0.6 and σ=0.1 Probability distribution with μ=0.6 and σ=0.3 Probability distribution with μ=0.7 and σ=0.4

Consider the joint pmf p(x,y) and marginal pmfs p(x) and p(y) for two discrete random variables X and Y as displayed in the table below. X p(x,y) 1 2 3 p(y) 1 0.125 0.0625 0.1875 0.125 0.5 Y 2 0.0625 0.0625 0.125 0.25 0.5 p(x) 0.1875 0.125 0.3125 0.375 1