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- In a sample of size 36, the sample mean was found to be 54.6. If the probability of getting a sample mean greater than 66.24 is 0.834, what is the standard deviation for sample means? O A. 72 O B. 3.464 O C. 8.485 O D. There is not enough information to find the sample standard deviation O E. 12Suppose that the number of points scored in a game comes from a normal population with an average of 12 points and a standard deviation of 9 points. Estimate the chance that the average points scored in ten randomly selected games will exceed 14.2 points. A. 0.4034 B. 0.0073 C. 0.2198 D. 0.2297A sample mean for a treated group of n = 9 individuals is 32 and the population mean for the untreated group is 26. If the sample standard deviation is 9 ( is unknown), which of the following test statistics is correct? O z = .67 O z = 2.0 Ot=.67 O t = 2.0
- After numerous studies, it is estimated that the age of college students follows a normal distribution with a mean of 20.7 years and a standard deviation of 1.8 years. A random sample of 16 college students is taken and the sample mean and sample standard deviation are found to be 21.5 years and 2.3 years, respectively. a.Is the sample average of 21.5 considered an outlier (in other words, what is the chance of getting a sample mean at least as large as 21.5 assuming μ and σ are correct)? b. The calculated value of the sample standard deviation is larger than σ, is 2.3 years enough larger than 1.8 that the estimate of σ does not seem reasonable? Use probability to support your conclusion c.No matter what you got for an answer in part b, assume we no longer trust σ = 1.8 to be valid. Calculate the same probability as you did in part a, but this time, assume that σ is unknown.The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 38 and a standard deviation of 9. Suppose that one individual is randomly chosen. Let X-percent of fat calories. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected fat calorie percent is more than 44. Round to 4 decimal places. c. Find the minimum number for the upper quartile of fat calories. Round to 2 decimal places.2. The owner of a factory that sells a particular bottled fruit juice claims that the average capacity of their product is 250 ml. To test the claim, a consumer group gets a sample of 100 such bottles, calculates the capacity of each bottle, and then finds the mean capacity to be 248 ml. The standard deviation is 5 ml. Is the claim true?
- The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.59 inches and a standard deviation of 0.03 inch. A random sample of 11 tennis balls is selected. 1. What is the probability that the sample mean is between 2.57 and 2.61 inches? 2. The probability is 63% that the sample mean will be between what two values symmetrically distributed around the population mean? 3. What is the probability that the sample mean is less than 2.56 inches?The plasticity of a polyethylene is affected by the concentration of a solution. When low concentration of the solution is used, the true mean plasticity is 55. And when high concentration is used, the mean plasticity is 62. The standard deviation of plasticity is 4 regardless of concentration of the solution. If two random samples of size 18 are taken, find the probability that Xhigh – X low 2 5. Include your solutions. O a. Probability is about 98% O b. Probability is about 7% O. NONE O d. Probability is about 93%3. Assume the heights of students at Champlain College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting a Champlain College studenttallerthan 62.2 inches?A. 0.0668B. 0.0359C. 0.9332D. 0.9641E. 1.0155
- 3. The braking distance for a Krazy-Car traveling at 50 mph is normally distributed with a mean of 50 ft. and a standard deviation of 5 ft. Answer the following without using a calculator or a table. • What is the likelihood a Krazy-Car will take more than 65 ft. to stop? • What is the probability a Krazy-Car will stop between 45 ft. and 55 ft.? • What percent of the time will a Krazy-Car traveling at 50 mph stop between 35 and 55 ft.? • What is the probability a Krazy-Car will require less than 50 ft. or more than 60 ft. to stop?1.In a certain wildlife reserve the life span of monkey are normally distributed. The average monkey lives 20.8 years and The standard deviation is 3.1 years. Use the empirical rule to estimate the probability or percentage of a monkey living less than 23.9 years. 2. If the population of the monkey are 568, how many of them will live for less than 23.9 years. 3. IQ scores which are normallu distributed have a mean of 100 and a standard deviation of 16. The z score that corresponds to Albert IQ Is 3.75. What is his IQ?3. The average height of a male student in the EDA class of Engr. Ventura in PLM has historically been 1.625 meters with a standard deviation of 0.07 meter. Is there a reason to believe that there has been a change in the average height of male EDA students under Engr. Ventura if a random sample of 50 males in the present EDA class has an average height of 1.652 meters? Assume the standard deviation remains the same.