Question

MATH 23 - TST Please show your work. No points can't read. Write clear final answer for each p ork. No points will be given for answers without explanation nor for work clear final answer for each problem (in words or using symbols ) The depth of annual snow fall in a mountain community is normally distributed with is chosen at random. mean μ .: 180 inches and standard deviation σ 30 inches. A year 50 the probability that the depth of the annual snowfall for the year will be greater 2. On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that bus will have fewer than 42 passengers 3. A survey found that the American family generates an average of 17.2jpounds of glass garbage each year. Assume that standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds. Assume that the sample is taken from a population normally distributed. 4. The 'average annual precipitation for a large Midwest city is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed Find the probability that the mean of a random sample of 32 months will have a mean less than 30 inches. 5, An insurance company says that 15% of all fires are caused by arson. a) Find the probability that among 5 fires exactly 2 are caused by arson. b) Find the expected number and standard deviation of arson fires out of 25 A new serum is claimed to be 80% effective in preventing the commou cold. A random sample of 11 people are injected with the serum. The serum is considered successful if someone who has taken it survives the winter without a cold. a) Find the probability that more than 8 people injected will survive the winter without a cold. b) If 100 people are injected, find the expected number ( who will survive the winter without a cold. 6 mean) of people in this sample

Answer 1

Step 1: Sketch the curve The probability that X 250 is equal to the blue area under the curve 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.002 80 100 120 140 160 180 200 220 240 260 280 Step 2 Since μ--180 and σ 30 we have 250-180 P(X>250 ) μ > 250-180-P ( X-μ P(X- Since Z- and 250 180 2.33 we have 30 P (X 250) P (Z 2.33) Step 3: Use the standard normal table to conclude that: P (Z > 2.33) 0.0099

Please post rest questions again

You are allowed to post one question a time by HomeworkLib policy

Please rate