On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.6 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , )? b. Find the probability that the child spends less than 1.6 hours per day unsupervised. ? c. What percent of the children spend over 2.3 hours per day unsupervised.? % (Round to 2 decimal places) d. 80% of all children spend at least how many hours per day unsupervised? hours. 2. On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 112 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N( , ) b. Find the probability that a randomly selected person's IQ is over 124?. (Round your answer to 4 decimal places.) c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? ( Round your answer to 2 decimal places). d. Find the Inter Quartile Range (IQR) for IQ scores.? (Round your answers to 2 decimal places.) Q1: Q3: IQR: 3. Suppose that the weight of seedless watermelons is normally distributed with mean 6.8 kg. and standard deviation 1.8 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. What is the median seedless watermelon weight? kg. c. What is the Z-score for a seedless watermelon weighing 7.7 kg? d. What is the probability that a randomly selected watermelon will weigh more than 7.5 kg? e. What is the probability that a randomly selected seedless watermelon will weigh between 6 and 6.5 kg? f. The 80th percentile for the weight of seedless watermelons is kg.? 4. Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(. , ) b. If one car is randomly chosen, find the probability that it is traveling more than 68 mph.? c. If one of the cars is randomly chosen, find the probability that it is traveling between 74 and 77 mph. ? d. 88% of all cars travel at least how fast on the freeway? mph. 5. In the 1992 presidential election, Alaska's 40 election districts averaged 2031 votes per district for President Clinton. The standard deviation was 570. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places. a. What is the distribution of X? X ~ N( , ) b. Is 2031 a population mean or a sample mean? Select an answer Sample Mean, Population Mean c. Find the probability that a randomly selected district had fewer than 1878 votes for President Clinton.? d. Find the probability that a randomly selected district had between 2062 and 2327 votes for President Clinton?. e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.?
1. On the planet of Mercury, 4-year-olds average 2.8 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.6 hours and the amount of time spent alone is
a. What is the distribution of X? X ~ N( , )?
b. Find the probability that the child spends less than 1.6 hours per day unsupervised. ?
c. What percent of the children spend over 2.3 hours per day unsupervised.? % (Round to 2 decimal places)
d. 80% of all children spend at least how many hours per day unsupervised? hours.
2. On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 112 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual.
a. What is the distribution of X? X ~ N( , )
b. Find the probability that a randomly selected person's IQ is over 124?. (Round your answer to 4 decimal places.)
c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? ( Round your answer to 2 decimal places).
d. Find the Inter
Q1:
Q3:
IQR:
3. Suppose that the weight of seedless watermelons is normally distributed with mean 6.8 kg. and standard deviation 1.8 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. What is the median seedless watermelon weight? kg.
c. What is the Z-score for a seedless watermelon weighing 7.7 kg?
d. What is the probability that a randomly selected watermelon will weigh more than 7.5 kg?
e. What is the probability that a randomly selected seedless watermelon will weigh between 6 and 6.5 kg?
f. The 80th percentile for the weight of seedless watermelons is kg.?
4. Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(. , )
b. If one car is randomly chosen, find the probability that it is traveling more than 68 mph.?
c. If one of the cars is randomly chosen, find the probability that it is traveling between 74 and 77 mph. ?
d. 88% of all cars travel at least how fast on the freeway? mph.
5. In the 1992 presidential election, Alaska's 40 election districts averaged 2031 votes per district for President Clinton. The standard deviation was 570. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers except part e. to 4 decimal places.
a. What is the distribution of X? X ~ N( , )
b. Is 2031 a population mean or a sample mean? Select an answer Sample Mean, Population Mean
c. Find the probability that a randomly selected district had fewer than 1878 votes for President Clinton.?
d. Find the probability that a randomly selected district had between 2062 and 2327 votes for President Clinton?.
e. Find the first quartile for votes for President Clinton. Round your answer to the nearest whole number.?
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