(b) Let x denotes the number of defective watch in a randomly selected box of a dozen of watches branded Fossel. 1 4 5 P(x) 0.45 0.25 0.16 0.09 0.03 0.02 Calculate the mean, variance as well as standard deviation of x. Compute the probability that the box contains at most two defective watches and interpret the answer. (ii) Compute the probability that the box contains less than two defective watches. Justify the lower probability value compared to answer in (ii). (ii1)
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- Suppose that a recent poll found that 48% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 350 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that t moral values is poor. The mean of X is. (Round to the nearest whole number as needed.) The standard deviation of X is (Round to the nearest tenth as needed.) (b) Interpret the mean. Choose the correct answer below. O A. For every 350 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. O B. For every 350 adults, the mean is the range that would be expected to believe that the overall state of moral values is poor. O C. For every 350 adults, the mean is the minimum number of them that would be expected to believe that the overall state of moral values is po O D. For every 168 adults, the mean is the maximum number of them that would be…Hugo averages 41 words per minute on a typing test with a standard deviation of 7.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X = the number of words per minute on a typing test. Then, X - N(41, 7.5). Suppose Hugo types 45 words per minute in a typing test on Wednesday. The z-score when x = 45 is x = 45 is This z-score tells you that standard deviations to the (right/left) of the mean, Correctly fill in the blanks in the statement above. Select the correct answer below: Suppose Hugo types 45 words per minute in a typing test on Wednesday. The z-score when x = 45 is -0.533. This z-score tells you that x = 45 is 0.533 standard deviations to the left of the mean, 41. Suppose Hugo types 45 words per minute in a typing test on Wednesday. The z-score when x = 45 is -0.381. This z-score tells you that x = 45 is 0.381 standard deviations to the left of the mean, 41. Suppose Hugo types 45 words per minute in a typing test on Wednesday. The…The mean total cholesterol for a population of men between the ages of 20 and 29 is 180 micrograms per decilitre with a standard deviation of 37.4. A healthy total cholesterol level is less than 200, 200-240 is border line, and above 240 is dangerous. Assume the distribution is approximately Normal. For a randomly selected man from this group, what is the probability that his total cholesterol level is i. 200 or more? 1i. Between 200 and 240?
- Assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. (a) If 1 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute. (Round your answer to 4 decimal places) (b) If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 80 beats per minute. (Round your answer to 4 decimal places)Suppose that a recent poll found that 60% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 400 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is 240. (Round to the nearest whole number as needed.) The standard deviation of X is. (Round to the nearest tenth as needed.)The average THC content of marijuana sold on the street is 9.7%. Suppose the THC content is normally distributed with standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,a. What is the distribution of X? X ~ N(Correct,Correct) b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 8.4. c. Find the 65th percentile for this distribution. % Submit QuestionQuestion 7
- A company produces steel rods. The lengths of the steel rods are distributed with a mean of 102.3-cm and a standard deviation of 2-cm. For shipment, 7 steel rods are bundled together. Round all answers to four decimal places if necessary. Note: When writing the distributions, they should be of the form (mean, variance) a. What is the distribution of X? X ~ ( b. What is the distribution of X? X~ N( c. For a single randomly selected steel rod, find the probability that the length is between 102.5-cm and 103.5-cm. d. For a bundled of 7 rods, find the probability that the average length is between 102.5-cm and 103.5- cm. e. For part d), is the assumption of normal necessary? Yes NoThe time taken by employees at Grace Floral shop to put a bouquet together has a normal distribution with mean 26.4 minutes and standard deviation .8 minutes. (i) Find the probability that an employee chosen at random takes between 24.6 and 27.8 minutes to put a bouquet together. [5] (ii) 12% of employees take more than t minutes to put a bouquet together. (ii) Find the value of t.Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 52 feet. We randomly sample 49 fly balls. Part (a) If X = average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places. X-N 250 7.43 Part (b) What is the probability that the 49 balls traveled an average of less than 242 feet? (Round your answer to four decimal places.) Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. ▲▲ 270 230 O 230 ✓ 230 Part (c) 240 240 250 250 260 260 270 230 240 240 250 250 Find the 70th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.) ft 260 260 270 270 sig arnin
- A machine produces small rods and large rods. The diameters of small rods are normally distributed with mean 2 cm and standard deviation 0.12 cm. The diameters of large rods are normally distributed with mean 2.2 cm and standard deviation 0.15 cm. (i) Find the probability that a randomly chosen small rod has diameter greater than 2.15 cm. (ii) A box contains one small rod and one large rod. Find the probability that at least one of the rods has diameter greater than 2.15 cm.An elevator has a play card stating that the maximum capacity is 1980 pounds 12 passengers so 12 adult male passages can have a mean way of up to 1180÷12 = 165 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 165 lb. Assume that weights of males are normally distributed with a mean of 172 pounds and a standard deviation of 27 pounds. Does this elevator appear to be safe?