For problems 1b-e, record the technology commands you used to find your answer.
ID: 3314149 • Letter: F
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For problems 1b-e, record the technology commands you used to find your answer. For example, on a TI calculator you might use "normalcdf(72000, 73000, 76000, 3400". On StatCrunch you might use "Normal calculator, mean=76000, standard deviation=3400, x80000".
1. The average income in the District of Columbia (DC) is the highest in the nation. In 2013 the mean income in DC was $76,000 with a standard deviation of $35,000. a. Describe the sampling distribution of sample means for samples of size 200 taken from this population. (Remember this means discuss the shape, center, and standard error of the distribution.)
b. A sample of 200 DC residents is taken. Find the probability that the mean income of this sample is between $77,000 and $80,000.
c. A sample of 200 DC residents is taken. Find the probability that the mean income of the sample is less than $73,000.
d. Would it unusual to find a mean income of more than $80,000 in a sample of 200 DC residents? Why or why not?
e. Complete this sentence: It would be unusual to find a sample mean less than ____ in a sample of 200 DC residents.
2. Weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pounds and are Normally distributed.
a. What is the probability that one newborn baby will have a weight between 6.4 and 7.6 pounds?
b. Suppose a sample of 10 babies is taken. What is the probability that the mean weight of the sample is between 6.4 and 7.6
Math 10 Online Problem Set #10 For problems 1b-e, record the technology commands you used to find your answer. For example, on a TI calculator you might use "normalcdf(72000, 73000, 76000, 3400". On StatCrunch you might use "Normal calculator, mean- 76000, standard deviation-3400, x280000" 1. The average income in the District of Columbia (DC) is the highest in the nation In 2013 the mean income in DC was $76,000 with a standard deviation of $35,000. a. Describe the sampling distribution of sample means for samples of size 200 taken from this population. (Remember this means discuss the shape, center, and standard error of the distribution.) b. A sample of 200 DC residents is taken. Find the probability that the mean income of this sample is between $77,000 and $80,000. . A sample of 200 DC residents is taken. Find the probability that the mean income of the sample is less than S73,000. d. Would it unusual to find a mean income of more than $80,000 in a sample of 200 DC residents? Why or why not? e. Complete this sentence: It would be unusual to find a sample mean less than in a sample of 200 DC residents. 2. Weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pounds and are Normally distributed. a. What is the probability that one newborn baby will have a weight between 6.4 and 7.6 pounds? b. Suppose a sample of 10 babies is taken. What is the probability that the mearn weight of the sample is between 6.4 and 7.6 pounds? (NOTE: Your answers to questions a and b should NOT be the same.)Explanation / Answer
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2) a) Mean = 7
SD = 0.6
For the normal distribution, the values within onestandard deviation of the mean account for 68.27% of the set; while within two standard deviations account for 95.45%; and within three standard deviations account for 99.73%.
So, our values are 1SD away.
P = 0.6827
b) n =10
z1 = (6.4 - 7)/0.6/10
z1 = - 3.16
z2 = 3.16
P = 0.9984
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