Suppose you have a bucket of 150 balls: 47 red, 62 blue, and 41 green. Describe the distribution for the random variable X = “Number of green balls obtained with
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Suppose you have a bucket of 150 balls: 47 red, 62 blue, and 41 green. Describe the distribution for the random variable X = “Number of green balls obtained with a single draw”.
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- Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births. Number of Girls x,P(x)0,0.0021,0.0272,0.1163,0.2224,0.2695,0.2226,0.1017,0.0358,0.006 The mean is μ= girl(s)? (Round to one decimal place as needed.) The standard deviation is σ= girl(s). ? (Round to one decimal place as needed.)A quality control engineer at Shell visits 80 gas stations and collects a fuel sample from each. She measures the sulphur content in the gas and sorts the samples into 4 different batches. She finds: 19 samples with less than 180 ppm sulphur, 20 samples with between 180 and 230 ppm, 23 samples with between 230 and 280 ppm, and 18 samples with more than 280 ppm. Does the sulphur content of gas follow a normal distribution with a mean of 230 ppm and a standard deviation of 50 ppm at the 5% significance levelA population distribution has o =6. What position in this distribution is identified bya z-score = + 2.00?
- Cal Poly Pomona found that 15% of its students withdraw without completing Calculus I course. Assume that 30 students registered for the course. Let X be the number of students who withdraw. What distribution does X follow?About 79% of all female heart transplant patients will survive for at least 3 years. Eighty female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70%? Assume the sampling distribution of sample proportions is a normal distribution. pq The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to n The probability that the sample proportion surviving for at least 3 years will be less than 70% is| (Round to four decimal places as needed.)In 1995, the median price of a PC was $1200. Suppose that a random sample of100 persons who bought their PCs during that year recorded the amount spent (byeach of them) on his/her PC. State the approximate sampling distribution of ˆp, theproportion of persons who spent more than $1200 on a PC. Find the probabilitythat more than 60% of this group spent more than $1200. NOTE: Please explain each part, so the problem can be used as a Study Guide
