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Unformatted text preview: 2 Question 1 Q 5 points
Suppose that college faculty with the rank of professor at 2~year institutions earn an average
of $65,000 per year with a standard deviation of $4000.1n order to verify this salary level,a
random sample of 60 professors was selected from a personnel database for all 2—year insti— tutions in the United States. _
a) Describe the sampling distribution of the sample mean X. 0/3: (2:) O m Sa/Wbr/(Q '
Ll ' a 1; 2 ‘M 7‘5 . ‘JOOCV by 6.1—» w: M 651000) f,
. {60/
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b)What is the probability that the saw is greater than $ 67,500 ? D9 you have to make any assumptions?Explain.
“r ugby, *4, \le ‘ Malia can; wntp'lwbrz/J “43': mag, C» Lilla _/ UM Y> £7,590): 19(2) Wyzﬂgjp “9&0 \ I 000
Q3 +2 J ' ﬂ Ibo c) What is the probability that a randomly selected professor earns more than $67,500?
Do you have to make any assumptions?Explain. “(H X > 6‘1 W93 ! ) a, l\ T» make; _ waawwJi/aﬁbwml aihémmg 1.. Cami W00
“1/ “was «2‘s we areamam ,, I WVM‘ X M Wu» 3637 9W,» 49’s“ 9’2 MS ) r V . . N' ,. \by‘ \d . ‘W "\m . r W x > £11 5790) We) éliﬁwéﬁfiﬁ, Mg/ o, ,4; 5) 1 N 0, 9,3 4/7 .4700 egg
d)lf your random sample actually produced a sample mean of $ 67,500,
would you consider this unusual? What conclusion might you draw? l7(>7>>6¥,6w5~:10(2> *mmwowx F133 ‘l’gll'tg (/7 0,90 3 . '0
Question 2 , :76 L) points
It is known that 40% of the customers in a sporting goods store purchase a pair of running
shoesA random sample of 25 customers is selected.Assume thatcustomer’s purchases are
made independently. '
a)What probability distribution describes the number of customers who purchase running
shoes? (give the name and parameters) ‘ X f 5% wﬁwwm va’tf/MQC, me x3, Lubes b) What isthe probability that exactly 10 customers purchase running shoes? /_ t(xamipj?(Xé“@3~*PCtss>arrmsc.oyzfsgiéz c)What is the probability that no more than 15 customers purchase running shoes? KKK): out as) d) What is the probability that more than 8 but less than 15 customers purchase running
shoes? W_§<x<6>=€{ QKXéWL Wxém‘ H x551): 0.466s 0423—0691 ‘3 e)How many customers in the sample would you expect to purchase running shoes? Emzwz OH x95: l0 
v.‘ Question 3 points
A manufacturer of bike racks for cars claims that the assembly time for a particular model
is normally distributed with a mean of 1 hour and a standard deviation of 0.10 hours. a) Find the probability that it takes at most 1.3 hours to assemble a bike rack of this model. XMM(VLL:,[ > 5‘: 010 D ' 1..3—~/ )
7‘ C _}_ A far, ~
L? if X_\,%3 {72,010 Find the probability that it takes exactly 1 hour to assemble a bike rack of this model. 19(xrl):0. c) Find the probability that it takes between 0.8 hours and 1.1 to assemble a bike rack
of this model. I l ~ > a m? <><<m>zmogji <g< 77... _ I \ ~ J;
51> ’l’( ~14 2< l): My.» H24 L 0‘ We e 0.022247 : DWI” “N. d) Find the assembly time that exceeds 97 % of all other assembly times for bike racks
of this model. ‘ / . Question 4 points
SuppOse you work for an insurance company , and yen sell a $10,000 1~year term insurance
policy at an annual premium of $290.Actuarial tables Show that the probability of death
during the next year for a person of your customer’s age is 0.001. What is the expected gain for the policy of this type? W {20b \ Cj  a
Question 5 L2 points
State the Central Limit Theorem. Question 6
For each of the following sentences, choose Whether it is true or false: 1. { points The sampling distribution of the sample mean is exactly normally distributed,
regardless of the sample size n. We: W The variance Aof the distribution of the sample mean is 02/77,, Where 02 is the population
variance and n is the sample size. Tm. The Central Limit Theorem states, among other things, that the value of the sample
mean is equal to the population mean when the sample size is large. limes The sampling distribution of the sample mean is the distribution obtained from re—
peatedly extracting samples of size n from a population. W For a large sample, the distribution of the sample mean is approximately normal, with
mean equal to the pepulation mean and standard deviation equal to the population standard deviation divided by ﬁn; Tia/as The Central Limit Theorem states that the sampling distribution of the sample mean7
is approximately normal for large sample sizes. v4 lme, ...
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 Spring '08
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