#1 Points possible: 1. Total attempts: 3 of the sample mcan’X*^ar’
Which of the following statements about the sampling not true?
A) The distribution is normal regardless of the shape of the population distribution.
B) The distribution is normal regardless of the sample size, as long as the population dis n is normal.
C) The distribution's mean is the same as the population mean.
D) The distribution's standard deviation is smaller than the population standard
deviation.
E) All of the above statements are correct.
O Choice A O Choice B O Choice C O Choice D
O Choice E
#2 Points possible: 1. Total attempts: 3
Which of the following is true about sampling distributions?
O Sampling distributions are always nearly normal.
O Shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is.
O Sampling distribution of the mean is always right skewed since means cannot besmaller than 0.
O Sampling distributions get closer to normality as tb« sample size increases • • - h
5 Points possible: 1. Total attempts: 3 Mich of the following statements are true?
J- The sampling distribution of T has standard den*ti«m — ever if - population is not normally distributed. i **
ttt samPjin& distribution of x is normal if the population has a normal distribution.
HI. When n is large, the sampling distribution of x is approximately normal even if the population is not normally distributed. *
Olandll
Ol and III
Oil and III
Ol, II, and III
O None of the above gives the complete set of true responses.
#4 Points possible: 1. Total attempts: 3
Business Weekly,/?Q_ndiicred a survey of graduates from 30 top MBA programs. On the basis of the surve^assinne the mean annual salary for graduates 10 years after graduation is $166,000. A/(ume the standard deviation is $38,000. Suppose you take a simple random sample of 18 graduates. Round all answers to four decimal places If necessary.
a. What is the distribution of X ? X ~ N(,)
b. What is the distribution of x ? x ~ N(,)
c. For a single randomly selected graduate, find the probability that her salary is between
$162,765 and $175,843.__________________
d. For a simple random sample of 18 graduates, find the probability that the average salary is between $162,765 and $175,843.
e. For part d), is the assumption of normal necessary? O Yes O No
Possible: 1. Total attempts: 3
CNNBC I
Standard dadation*! ^7 the T* annual cost of aut0 insurance is 975 dollars. Assume the
sample of 35 ant -t • ° and the cost is normally distributed. You take a simple random
P ot 35 auto insurance policies. Round your answers to 4 decimal places.
* Mat is the distribution of X?X~N(_________________, )
b. What is the distribution of x ? X ~ N( , )
C. What is the probability that one randomly selected auto insurance is more than $1006?
d. a simple random sample of 35 auto insurance policies, find the probability that the average cost is more than $ 1006.
e. For part d), is the assumption of normal necessary? OYesONo
#6 Points possible:, 1. Total attempts: 3
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 26 weeks. Assume that the length of unemployment is normally distributed with population mean of 26 weeks and the population standard deviation of 2 wee s. Suppose you would like to select a random sample of 13 unemployed individuals for a follow-up study. Round the answers of following questions to 4 decimal places.
a. What is the distribution of X ? X ~ N()
b. What is the distribution of X ? X ~ N(_______,__________)
c. What is the probability that one randomly selected individual found a job more than 27
weeks? ________________
d. For 13 unemployed individuals, find the probability that the average time that they found
the next job is more than 27 weeks.______________
e. For part d), is the assumption of normal necessary? O Yes ONo
#7 Points possible: 1. Total attempts: 3
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 251.7-cm and a standard deviation of 1.5-cm. For shipment, 12 steel rods are bundled together. Round all answers to four decimal places if necessary.
a. What is the distribution of X1X ~ N(,)
b. What is the distribution of x ? x ~ N( )
c. For a single randomly selected steel rod, find the probability that the length is between
251.5-cm and 252.1-crn._________________
d. For a bundled of 12 rods, find the probability that the average length is between 251.5-cnt and 252.1-cm.
e. For part d), is the assumption of normal necessary? ONoO Yes
•8 Points possible: 1. Total attempts: 3
manager ot a computer retails store is concerned that his suppliers have been giving him laptop 3 «oL 4a«AMk4k|)f ftr
the model laptop of concern are normally distributed with a mean of 4.3 years and a standard deiation of 0.4 years. He then randomly selects records on 35 laptops sold in the past. Round the aasn ers of following questions ro 4 decimal places.
a. What is the distribution of X *! X ~ N(,)
K What is the distribution of 2 ? X ~ N(,)
c. What is the probability that one randomly selected laptop is replaced less than 4.4 years?
d. For 35 laptops, find the probability that the average replacement time is less than 4.4 year.
e. For part d), is the assumption of normal necessary? O No O Yes
#9 Points possible: 1. Total attempts: 3
Suppose the age that children learn to walk is normally disiribured with mean 12 months and standard deviation 1.3 month. 8 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
*. What is the distribution of X1X ~ N(,____________)
b. What is the distribution of 2 ? X ~ N(,__________)
c. What is the probability that one randomly selected person learned to walk when the person was between 11.5 and 13 months old?
d. For the 8 people, find the probability that the average age that they learned to walk is between 11.5 and 13 months old.
e. For part d), is the assumption that the distribution is normal necessary? O No O Yes
£ Find the IQR for the average first time walking age for groups of 8 people.
QI = months
Q3 =months
IQR: months
Ttiui unit,} pv33iijusj. i. lOual atternpt.5! 3
The lengths of adult males' hands are normally distributed with mean 186 mm and standard deviation is 7.2 mm. Suppose that 46 individuals arc randomly chosen. Round all answers to 4 where possible.
a. What is the distribution of x ? x ~ N(,)
b. For the group of 46. find the probability that the average hand length is more than 188.
c. Find the third quartile for the average adult male liand length for this sample size.
d. For part b). is the assumption that the distribution is normal necessary? O Yes ONo