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- A. The length of a statistics class taught by a particular professor is uniformly distributed between 45 and 55 minutes long. What is the probability that a class lasts longer than 49 minutes? B. The age that women in Virginia decide to get married for the first time is normally distributed with an average of 26.3 years and a standard deviation of 3.1 years. Suppose that 25 Virginian women are randomly selected and asked about their age at the beginning of their first marriage, find the probability that the sample mean age is between 25 and 28 years.In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Compute and interpret the mean of the random variable X Px = marriages (Type an integer or a decimal. Do not round.) Which of the following interpretations of the mean is correct? O A. If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be equal to the mean number of marriages for most individuals. OB. If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be less than the mean number of marriages for most individuals OC. If many randomly selected individuals 40 to 49 years of age were surveyed, the sample mean number of marriages should be close to the mean of the random variable. OD. If many individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of…According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze. Complete parts (a) through (c). (a) What is the probability that among 18 randomly observed individuals, exactly 5 do not cover their mouth when sneezing? Using the binomial distribution, the probability is 0.2050. (Round to four decimal places as needed.) (b) What is the probability that among 18 randomly observed individuals, fewer than 6 do not cover their mouth when sneezing? Using the binomial distribution, the probability is (Round to four decimal places as needed.)
- Example: Suppose the mean of the number of unproductive days for a certain large segment of the population in a given year is 5.4 and the standard deviation is 2.8 days. Find the probabilities that average number of unproductive days of a random sampling of 49 from this environment is: a. more than 6 days b. between 4 and 6 days.Suppose that from a random sample of size 24 sample mean and standard error of mean are found to be 35 and 5, respectively. Acoording to this information someone may assert with a probability of _______ that the true mean is between 32.5 and 37.5.A population has a mean of 50 and a standard deviation of 19 If a random sample of 36 is taken, what is the probability that the sample mean is each of the following? a . Greater than 50. b. less than 52. C. less than 49. d.between 45.5 and 54.5 e and Between 50.5 and 51.1
- 3Suppose that the mean hourly wage of all employees in a large semiconductor manufacturing facility is $50 with a standard deviation of $10. Let X be the mean hourly wages of certain employees selected randomly from all the employees of this manufacturing facility. If a random sample of 64 employees is selected, then the probability that the mean hourly wages X falls between $48 and $52 is: 0.9986 0.8904 0.9544 0.98981)30% of flowers of a certain species bloom early (before May 1st). You work for an arboretum and have a display of these flowers.In a row of flowers, what is the probability that you will observe more than 4 flowers before you see the first one that blooms early? Round your answer to four decimal place
- A poll asked people with and without children under 18 years old if they frequently experienced stress. The results are shown in the accompanying table. Complete parts (a) through (c) below. Frequently Experience Stress Yes No Total With child under 296 234 530 18 уears No child under 196 314 510 18 years Total 492 548 1040 a. Find the probability that a randomly chosen person from this group said "Yes," given that the person has a child under 18 years old. (Type an integer or decimal rounded to four decimal places as needed.) b. Find the probability that a randomly chosen person from this group said "Yes," given that the person does not have a child under 18 years old. (Type an integer or decimal rounded to four decimal places as needed.) c. Find the probability that a randomly chosen person from this group said "Yes" or had a child under 18 years old. (Type an integer or decimal rounded to four decimal places as needed.). According to one study, 15% of workers call in sick on their birthdays. A random sample of 11 workers is selected.a. What is the probability that at most 2 of the workers in the sample call in sick on their birthdays?b. Find the expected value and standard deviation (rounded to 2 decimal places)Q25.If the records show that, the probability of failing (with grade F) this course is p, [use the answer of question 22 above as the probability, p, here], what is the probability that at most 2 students out of 16 fail this course? {Hint: use binomial distribution}