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- 1Assume a binomial probability distribution has p = .60 and n = 200.a. what are the mean and standard deviation?b. Is this situation one in which binomial probabilities can be approximated by thenormal probability distribution? Explain.c. what is the probability of 100 to 110 successes?d. what is the probability of 130 or more successes?e. what is the advantage of using the normal probability distribution to approximate thebinomial probabilities? Use part (d) to explain the advantage.According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X- NO b. Find the probability that the person is between 64.4 and 67.3 inches. c. The middle 50% of Martian heights lie between what two numbers? Low: inches inches High:
- d) Which number of minutes per day represents the 70th percentile?  (Round to the nearest whole number as needed.)CNNBC recently reported that the mean annual cost of auto insurance is 956 dollars. Assume the standard deviation is 280 dollars, and the cost is normally distributed. You take a simple random sample of 38 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N( b. What is the distribution of T? T - N( c. What is the probability that one randomly selected auto insurance is more than $906? d. a simple random sample of 38 auto insurance policies, find the probability that the average cost is more than $906. e. For part d), is the assumption of normal necessary? O YesO NoAccording to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the person is between 62 and 63.9 inches. c. The middle 40% of Martian heights lie between what two numbers? Low: inches High: inches
- CNNBC recently reported that the mean annual cost of auto insurance is 968 dollars. Assume the standard deviation is 259 dollars, and the cost is normally distributed. You take a simple random sample of 36 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X? X - N( b. What is the distribution of ? T - N( c. What is the probability that one randomly selected auto insurance is less than $1015? d. a simple random sample of 36 auto insurance policies, find the probability that the average cost is less than $1015. e. For part d), is the assumption of normal necessary? O YesO No3. Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is between a 6 and a 9?Private nonprofit four-year colleges charge, on average, $26,168 per year in tuition and fees. The standard deviation is $6,656. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 24,347 per year. c. Find the 74th percentile for this distribution. $ (Round to the nearest dollar.)
- The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.5 ppm and standard deviation 1.7 ppm. 37 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of ? ¤ - N( c. What is the probability that one randomly selected city's waterway will have more than 9.8 ppm pollutants? d. For the 37 cities, find the probability that the average amount of pollutants is more than 9.8 ppm. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes f. Find the IQR for the average of 37 cities. Q1 = ppm Q3 = ppm IQR: ppm24)The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15days. a. Find the probability of a pregnancy lasting 309 days or longer. b. If the length of pregnancy is in the lowest 3%,then the baby is premature. Find the length that separates premature babies from those who are not premature.