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10) Suppose that the actual amount of instant coffee that a filling machine puts into "125 c.c. "cups is a normal random variable with a mean $$\mu$$, and a standard deviation $$\sigma=5.102$$ c.c. If $$2.5 \%$$ of the cups overflow, what percentage of the cups will contain less than 110 c.c. a) $$2.5 \%$$ b) $$16.35 \%$$ c) $$33.65 \%$$ d) None of these 11) A firm is placing three different orders for supplies among three different distributors. Each order is randomly assigned to one of the distributors, and a distributor can receive more than one order. Find the probability that all the three orders go to the same distributor. $$\begin{array}{llll}\text { a) } \frac{6}{27} & \text { b) } \frac{1}{27} & \text { c) } \frac{3}{27} & \text { d) None of these }\end{array}$$ 12) The members of a consulting firm rent cars from two cars rental agencies, $$60 \%$$ from agency $$X_{\text {and }} 40 \%$$ from agency $$Y$$. It is known that $$10 \%$$ of the cars rented from agency $$X$$ need a tune-up, and $$\%$$ the consulting firm was found to need a tune-up, what is the probability that it was rented from agency $$X$$ ? $$0.25$$ brobability that $$\begin{array}{lll}\text { a. } 0.75 & \text { b) } 0.25 & \text { c) } 0.08\end{array}$$ 7) $$A$$, and $$B$$ are two independent events. If $$P(A)=0.6, P(A \cup B)=1$$, then $$P(A \cap f)$$ equals a) $$0.6$$ b) $$0.0$$ c) $$0.16$$ d) None of these 8) A pair of fair dice are rolled till getting sum $$=7$$. Let $$X$$ a random variable representing the number of rolls required to get sum 7 for the first time. What is $$P(X>2)$$ ? a) $$0.0067$$ b) $$0.0278$$ c) $$0.6944$$ d) None of these 9) Suppose that $$X$$ is an exponential random variable. If $$P(X \geq 10)=0.1353$$, then $$P(10 \leq$$ $$X \leq 15$$ ) equals approximately a) $$0.1353$$ b) $$0.0608$$ c) $$0.0855$$ d) None of these 20) Seprese thur $$50 \ 5$$ of the $$\mathrm{NDU}$$ students have GPA $$\geq 2.75$$. If $$100 \mathrm{NDU}$$ students were mading selveded approximate the probability that at most 55 of them will have a) 03643 b) $$0.3528$$ c) $$0.3413$$ d) None of these A random sample of size $$n=25$$ selected from a normal population with unknown (30 $$u$$ and a known variance $$\sigma^{2}=9$$, shows $$\bar{x}=21.25$$, If we set $$\mu=\bar{x}=21.25$$, then We are $$95 \%$$ confident that the maximum error of estimate equals $$1.176$$ We are $$90 \%$$ confident that the maximum error of estimate equals $$0.987$$ Both parts (a) and (b) are true None of these is true 18) If $$X$$ and $$Y$$ be two continuous random variables with joint probability density function \[ f(x, y)=\left\{\begin{array}{lr} \frac{1}{2} & \text { for } 0\frac{P \text {-vatue }}{2} \) b) Reject the claim since the given value of $$a p$$ - value 25) We have a normal population with unknown mean $$\mu$$ and unknown variane $$a^{1}$$. Suppose we are testing $$H_{0}: \mu=55$$ against $$H_{1}: \mu \neq 55 \quad$$ at $$\alpha=0.05$$ If random sample of size 16 shows $$x=57$$ and $$S^{2}-15.5$$, then we should a. Reject $$H_{0}$$, since O.V.T.S $$=7.75$$ and is not between $$-2.131$$ and $$2.131$$ b. Accept $$H_{0}$$, since O.V.T.S $$=1.96$$ and is between $$-2.201$$ and $$2.201$$ d. Reject $$H_{0}$$, since O.V.T.S $$=2.032$$ and is not between $$-1.96$$ and $$1.96$$ 26) Suppose we have a normal population with a known mean $$\mu=55$$, and unknown variance $$\sigma^{2}$$. We are testing the claim that $$\sigma=6$$. If a random sample of size 16 selected from the population shows $$\bar{x}=40$$, and $$S=7$$, then the value of O.V.T.S equals a) $$10.417$$ b) $$5.714$$ c) $$20.417$$ d) None of these 21) In testing the claim $$\mu=107$$, type I error happens when we a) Reject the claim $$\mu=107$$, when actually the claim is not true b) Accept the claim $$\mu=107$$, when actually the claim is true c) Reject the claim $$\mu=107$$, when actually the claim is true d) Accept the claim $$\mu-407$$, when actually the claim is not true 22) Suppose we are testing $$H_{0}: \mathrm{P}=0.69$$, against $$H_{1}: \mathrm{P} \neq 0.69 \quad$$ at $$\alpha=0.05$$ A random sample of 220 were selected. The sample shows $$\hat{p}=0.75$$. What is the $$P$$ - value of the test? a) $$0.0548$$ b) $$0.0274$$ c) $$0.0239$$ d) $$0.0478$$ 23) Suppose we have a normal population with unknown variance $$\sigma^{2}$$, and we are testing $$H_{0}: \sigma^{2}=25$$ against $$H_{a}: \sigma^{2}<25 \quad$$ at $$\alpha=0.05$$ If a random sample of size 11 was selected and the observed value of the test statistic "O.V.T.S" was calculated to be $$3.29$$, then we shall a) Accept $$\mathrm{H}_{0}$$, since O.V.T.S $$<18.307$$ b) Reject $$H_{0}$$, since O.V.T.S $$<3.94$$ c) Accept $$H_{0}$$, since O.V.T.S $$<4.575$$ d) Reject $$H_{0}$$, since O.V.T.S $$<18.307$$ Page 12 of 1 b) The samplesieentemath c) The sample viov in is large d) The sample siee it is small and the population standard deviation $$\sigma$$ is unknown 28) Sugwow that the GPI of the $$\mathrm{NDU} /$$ mudenis is known to have a mean of $$2.9$$, and a standard deviation of $$0.12$$. If a random sample of 30 students was selected, then the Truhabition a) 0 (M)o b) $$0.4504$$ e) $$0.0 \mathrm{NOH}$$ d) None of the above 20) Suppose that $$50 \%$$ of the NDU students have GPA 2 2.75. If $$100 \mathrm{NDU}$$ students were randomly selected, approximate the probability that at most 55 of them will have $$G P A \leq 2.75$$ a) $$0.3643$$ b) $$0.3528$$ c) $$0.3413$$ d) None of these 12) A random sample of size $$n=25$$ selected from a normal population with unknown (30 mean $$\mu$$ and a known variance $$\sigma^{2}=9$$, shows $$x=21$$, 25, If we set $$\mu=x=21.25$$, then a) We are $$95 \%$$ confident that the maximum error of estimate equals $$1.176$$ b) We are $$90 \%$$ confident that the maximum error of estimate equals $$0.987$$ c) Both parts (a) and (b) are true d) None of these is true

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