Problem 7 The average yearly Philhealth benefit per person was 4,064 php in a recent year. If the benefits are normally distributed with a standard deviation of 460 php, find the probability that the mean benefit for a random sample of 20 persons is: a) Less than 3800 php b) More than 4100 php
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- Problem 15 The heights of two-story townhouses in a small city are known to be uniformly distributed between 20 feet and 28 feet. nthe a) Find the probability that a randomly selected two-story townhouse has a height that exceeds 25 feet. b) Find the mean and the variance of the distribution of the heights of two-story townhouses in that city. Duoblonm 16Problem 6 The average travel time (one way) from National University to Robinsons Magnolia is 25 minutes according to a survey conducted by NU engineering students. If we assume that commuting times are normally distributed and that the standard deviation is 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes from NU to Robinsons Magnolia? Less than 18 minutes?Problem 3) Lead concentrations in the eggshells of California condors have a mean of 1.8 and a standard deviation of 0.3 ppm. The contamination levels of eggshells are classified as "low" if the lead concentration is below 1.0 ppm, “moderate" if the lead concentration falls between 1.0 ppm and 2.4 ppm, and “high" the lead concentration is above 2.4. Assuming that the lead concentrations of eggshells follows a normal distribution, answer the following questions. (Hint* The categories of Low, Moderate, and High can help you identify the boundaries of each interval. For example, the boundaries of Low are – ∞ to 1.0.) ppm 13. What is the percentile of an eggshell with a lead concentration of 2.3 ppm? a. 81st b. 93rd с. 86th d. 95th 14. What lead concentration corresponds to the 79th percentile? a. 2.04 ppm b. 2.53 ppm с. 2.43 рpm d. 2.76 ppm
- QUESTION 3 Two classes A and B of 200 students each take the same examination, out of 100 points. The average grade for class A is 80 with a standard deviation of 10 point s. The average grade for class B is 75 with a standard deviation of 15 points. Assume that the grades in both classes are normally distributed. If the passing grade is 60, how many more students passed the examination in class A than in class B?Problem 26. Boxes of Instant Dinner have a marked weight of 12.2 oz. In reality, the weights of the boxes are normally distributed with a mean of 12.8 oz and a standard deviation of 0.3 oz. Use the 68-95-99.7 Rule to determine the percent of the boxes that contain more than 12.2 oz.Question 2: Arandom variable is distributed normally with mean 3200 and standard deviation 800. Determine the probability of greater than 4000?
- question 2b. The annual yield (expressed as a percentage) for all investments in a particular asset class in the latest financial year was normally distributed with a mean of 4.5% and a standard deviation of 1.25%.i. Represent the probability that a randomly selected investment in this class will have an annual yield greater than 6.00%on a diagram and determine this probability. ii. Represent the value for annual yield that only 10% of investments in this class exceed on a diagram and determine this value.Question 2: If X is normally distributed with mean 32 and standard deviation 4. Find the probability that xis at least 36?Question 2 (a) A HR manager would like to survey the salary of the junior accountant in Malaysia to analyse the market trend. He found that it is normally distributed with a population mean of RM 2900 and a population standard deviation of RM 250. One day, he selects a random sample of the salaries of 30 junior accountants. (i) What is the probability that the sample mean salary will be between RM 2800 and RM 3000? What is the probability that the sample mean salary will be below RM 2850? (ii) (iii) The probability is 99% that the sample mean salary of the junior accountant will be between which two values (symmetrically distributed around the mean)? (iv) Do you think he will be likely to get the sample mean salary more than RM 3200? Justify your answer with probability.
- Problem 3: The mean yearly mileage of the vehicles in a delivery company's fleet is 51,400 miles, with a standard deviation of 4,800 miles. You take a random sample of 30 vehicles and another of 45 vehicles. What is the probability that the difference between the mean mileage of the two samples will be a) less than 2,000 miles? b) More than 500?PROBLEM 1: According to the Commission on Higher Education, College professors work for an average of 43 hours per week during a semester. A dean of Universify X surveys 25 randomly selected professors and found out that they work for an average of 45 hours a week with a standard deviation of 7 hours. Test if the mean number of professors' work hours worked recorded by the dean of University X differs from the recorded national average. Use a = 0.01 Formulate the hypothesis 1. Ho: 2. HA: 3. Given: 5. Solve for t: S = n = a = 4. Test statistics: 7. d. f. = 8. Solve the critical value (te) 6. t = 10. 9. Te12. How many miles will be traveled by at least 50% of the trucks? (Hint: Draw a graph.) lidadong eri bai zdl 8 bas 0T 13. How many miles will be traveled by at least 80% of the trucks? (Hint: Draw a graph.) rilidadonq od ba
