Q1: A distribution of numbers is approximately bell shaped. If the mean of the n
ID: 3318410 • Letter: Q
Question
Q1: A distribution of numbers is approximately bell shaped. If the mean of the numbers is 130 and the standard deviation is 10,
a. between what two numbers would approximately 68% of the values fall?
b. Between what two numbers would 95% of the values fall?
c. Between what two values would 99.7% of the values fall?
Q2: The Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a college degree, the mean before-tax family income is $ 85,100. Suppose that 54% of the before-tax family incomes when the head of the household has a college degree are between $75,500 and $94,700 and that these incomes are normally distributed. What is the standard deviation of before-tax family incomes when the head of the household has a college degree?
Q3:
(1) P(x 70 | = 50 and = 7)
(2) P(x > 43 | = 50 and = 5)
(3) P(18 < x < 22 | = 20 and = 3)
Q4: According to an NRF survey conducted by BIGresearch, the average family spends about $237 on electronics (computers, cell phones, etc.) in back-to-college spending per student. Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54. If a family of a returning college student is randomly selected, what is the probability that:
(a) They spend less than $135 on back-to-college electronics?
(b) They spend more than $340 on back-to-college electronics?
(c) They spend between $115 and $175 on back-to-college electronics?
Q5: Suppose the average speeds of passenger trains traveling from Newark, New Jersey, to Philadelphia, Pennsylvania, are normally distributed, with a mean average speed of 89 miles per hour and a standard deviation of 6.3 miles per hour.
(a) What is the probability that a train will average less than 73 miles per hour?
(b) What is the probability that a train will average more than 78 miles per hour?
(c) What is the probability that a train will average between 90 and 98 miles per hour?
Q6: Suppose commute times in a large city are normally distributed and that 61.00% of commuters in this city take more than 21 minutes to commute one-way. If the standard deviation of such commutes is 6.0 minutes, what is the mean commute?
Explanation / Answer
As per the Chegg policy, we are advised to do only one question at a time so i am attempting the 1st one.
1. As per the Empirical rule,
68% of the data lies within 1 standard deviation from the mean.
95% of the data lies within 2 standard deviation from the mean.
99.7% of the data lies within 3 standard deviation from the mean.
Therefore,
a) Approx 68% of the data falls between (130 - 10) and (130 + 10) i.e. 120 and 140
b) Approx 95% of the data falls between (130 - 2*10) and (130 + 2*10) i.e. 110 and 150
c) Approx 99.7% of the data falls between (130 - 3*10) and (130 + 3*10) i.e. 100 and 160
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