Probability Distributions Exercise 7.4

Dear Class 12 Samacheer Kalvi students, here are the Text Book Solutions for Exercise 7.4 Business Maths Chapter 7 Probability Distributions for your reference and study.

You can find links to the other exercises below.

Probability Distributions Important Formulas

Solutions for Probability Distributions Exercise 7.1

Solutions for Probability Distributions Exercise 7.2

Solutions for Probability Distributions Exercise 7.3

Probability Distributions Exercise 7.4

$\text{1. Normal distribution was invented by} \\$

$(a) \; Laplace \\$
$(b)\; De-Moivre \\$
$(c)\; Gauss \\$
$(d)\; \text{all the above}$

$Ans: \;(b)\; De-Moivre \\$

$2. \text{If X }\sim N(9,81)\; \text{the standard normal variate Z will be} \\$

$(a) \; Z=\frac{X-81}{9} \\$
$(b)\; Z=\frac{X-9}{81} \\$
$(c)\; Z=\frac{X-9}{9} \\$
$(d)\; Z=\frac{9-X}{9}$

$Ans: \; (c)\; Z=\frac{X-9}{9}\\$

$\text{3. If Z is a standard normal variate, the proportion of items lying } \\$
$\text{between Z = -0.5 and Z = -3.0 is} \\$

$(a) \; 0.4987 \\$
$(b)\; 0.1915 \\$
$(c)\; 0.3072 \\$
$(d)\;0.3098$

$Ans: \;(c)\; 0.3072 \\$

$\text{4. If} \; X \sim N(μ, σ2), \text{the maximum probability} \\$
$\text{at the point of inflexion of normal distribution is}\\$

$(a) \; \left( \frac{1}{\sqrt{2 \pi}} \right)^{e^{\frac{1}{2}}} \\$
$(b)\; \left( \frac{1}{\sqrt{2 \pi}} \right)^{e^{\frac{-1}{2}}} \\$
$(c)\;\left( \frac{1}{\sigma\; \sqrt{2 \pi}} \right)^{e^{\frac{-1}{2}}} \\$
$(d)\; \frac{1}{\sqrt{2 \pi}}$

$Ans: \; (c)\;\left( \frac{1}{\sigma\; \sqrt{2 \pi}} \right)^{e^{\frac{-1}{2}}} \\$

$\text{5. In a parametric distribution the mean is equal to variance is} \\$

$(a) \; binomial \\$
$(b)\; normal \\$
$(c)\; poisson \\$
$(d)\; \text{all the above}$

$Ans: \; (c)\; poisson \\$

$\text{6. In turning out certain toys in a manufacturing company, the } \\$
$\text{average number of defectives is} \; 1\%. \; \text{The probability that the } \\$
$\text{sample of 100 toys there will be 3 defectives is} \\$

$(a) \; 0.0613 \\$
$(b)\; 0.613 \\$
$(c)\; 0.00613 \\$
$(d)\; 0.3913$

$Ans: \; (a) \; 0.0613 \\$

$\text{7. The parameters of the normal distribution} \\$
$f(x)=\frac{1}{\sqrt{72\pi}}\frac{e^{-(x-10)^{2}}}{72} -\infty < X < \infty \\$

$(a) \; (10,6) \\$
$(b)\; (10,36) \\$
$(c)\; (6,10) \\$
$(d)\; (36,10)$

$Ans: \;(b)\; (10,36) \\$

$\text{8. A manufacturer produces switches and experiences that 2 per cent } \\$
$\text{switches are defective. The probability that in a box of 50 switches, } \\$
$\text{there are atmost two defective is :} \\$

$(a) \; 2.5\; e^{-1} \\$
$(b)\; e^{-1} \\$
$(c)\; 2\; e^{-1}\\$
$(d)\; \text{none of the above}$

$Ans: \; (a) \; 2.5\; e^{-1} \\$

$\text{9. An experiment succeeds twice as often as it fails. The chance that} \\$
$\text{in the next six trials, there shall be at least four successes is}\\$

$(a) \; \dfrac{240}{729} \\$
$(b)\; \dfrac{489}{729} \\$
$(c)\; \dfrac{496}{729} \\$
$(d)\; \dfrac{251}{729}$

$Ans: \;(c)\; \frac{496}{729} \\$

$\text{10. If for a binomial distribution B(n,p) mean = 4 and variance = 4/3, the} \\$
$\text{probability,} \; P(X \ge 5) \text{is equal to}\; \\$

$(a) \; \left( \frac{2}{3} \right)^{6} \\$
$(b)\; \left( \frac{2}{3} \right)^{5}\left( \frac{1}{3} \right) \\$
$(c)\; \left( \frac{1}{3} \right)^{6} \\$
$(d)\; 4 \left( \frac{2}{3} \right)^{6}$

$Ans:\; (d)\; 4 \left( \frac{2}{3} \right)^{6}\\$

$\text{11. The average percentage of failure in a certain examination is 40. The probability}\\$
$\text{ that out of a group of 6 candidates atleast 4 passed in the examination are} \\$

$(a) \; 0.5443 \\$
$(b) \; 0.4543 \\$
$(c) \;0.5543 \\$
$(d)\; 0.4573$

$Ans:\; (a) \; 0.5443 \\$

$\text{12. Forty percent of the passengers who fly on a certain route do not check in }\\$
$\text{any luggage. The planes on this route seat 15 passengers. For a full flight, what }\\$
$\text{is the mean of the number of passengers who do not check in any luggage?}\\$

$(a) \; 6.00 \\$
$(b)\; 6.45 \\$
$(c)\; 7.20 \\$
$(d)\; 7.50$

$Ans:\; (a) \; 6.00 \\$

$\text{13. Which of the following statements is/are true regarding} \\$
$\text{the normal distribution curve?} \\$

$(a) \; \text{it is symmetrical and bell shaped curve}\\$
$(b)\;\text{it is asymptotic in that each end approaches the horizontal axis} \\$
$\text{but never reaches it} \\$
$(c)\;\text{its mean, median and mode are located at the same point} \\$
$(d)\;\text{all of the above statements are true.}$

$Ans:\; (d)\;\text{all of the above statements are true.}\\$

$\text{14. Which of the following cannot generate a Poisson distribution?}\\$

$(a) \; \text{The number of telephone calls received in a ten-minute interval}\\$
$(b)\; \text{The number of customers arriving at a petrol station} \\$
$(c)\; \text{The number of bacteria found in a cubic feet of soil} \\$
$(d)\; \text{The number of misprints per page}$

$Ans:\;(b)\; \text{The number of customers arriving at a petrol station} \\$

$\text{15. The random variable X is normally distributed with a mean of 70 and a}\\$
$\text{standard deviation of 10. What is the probability that X is between 72 and 84?}\\$

$(a) \; 0.683 \\$
$(b)\; 0.954 \\$
$(c)\; 0.271 \\$
$(d)\;0.340$

$Ans:\; (d)\;0.340 \\$

$\text{16. The starting annual salaries of newly qualified chartered accountants (CA's) }\\$
$\text{in South Africa follow a normal distribution with a mean of Rs. 1,80,000 and a }\\$
$\text{standard deviation of Rs.10,000. What is the probability that a randomly selected}\\$
$\text{newly qualified CA will earn between Rs.1,65,000 and Rs. 1,75,000 per annum?}\\$

$(a) \; 0.819 \\$
$(b)\; 0.242 \\$
$(c)\; 0.286 \\$
$(d)\;0.533$

$Ans: \;(b)\; 0.242 \\$

$\text{17. In a large statistics class the heights of the students are normally} \\$
$\text{ distributed with a mean of 172cm and a variance of 25cm. What proportion} \\$
$\text{ of students are between 165cm and 181cm in height?} \\$

$(a) \; 0.954 \\$
$(b)\; 0.601 \\$
$(c)\; 0.718 \\$
$(d)\;0.883$

$Ans:\;(d)\;0.883 \\$

$\text{18. A statistical analysis of long-distance telephone calls indicates that}\\$
$\text{the length of these calls is normally distributed with a mean of 240 seconds }\\$
$\text{and a standard deviation of 40 seconds. What proportion of calls lasts less }\\$
$\text{than 180 seconds?}\\$

$(a) \; 0.214\\$
$(b)\; 0.094 \\$
$(c)\; 0933 \\$
$(d)\;0.067$

$Ans:\; (d)\;0.067 \\$

$\text{19. Cape town is estimated to have }\; 21\% \; \text{of homes whose owners }\\$
$\text{subscribe to the satelite service, DSTV. If a random sample of your home}\\$
$\text{is taken, what is the probability that all four home subscribe to DSTV?}\\$

$(a) \;0.2100 \\$
$(b)\; 0.5000\\$
$(c)\; 0.8791 \\$
$(d)\;0.0019$

$Ans: \;(d)\;0.0019 \\$

$\text{20. Using the standard normal table, the sum of the probabilities to } \\$
$\text{the right of z = 2.18 and to the left of z = -1.75 is} \\$

$(a) \; 0.4854 \\$
$(b)\; 0.4599 \\$
$(c)\; 0.0146 \\$
$(d)\; 0.0547$

$Ans:\; (d)\; 0.0547\\$

$\text{21. The time until first failure of a brand of inkjet printers is normally}\\$
$\text{distributed with a mean of 1,500 hours and a standard deviation of 200 hours. }\\$
$\text{What proportion of printers fails before 1,000 hours?}\\$

$(a) \; 0.0062 \\$
$(b)\; 0.0668 \\$
$(c)\; 0.8413 \\$
$(d)\; 0.0228$

$Ans:\; (a) \; 0.0062 \\$

$\text{22. The weights of newborn human babies are normally distributed with a }\\$
$\text{mean of 3.2kg and a standard deviation of 1.1kg. What is the probability that }\\$
$\text{a randomly selected newborn baby weighs less than 2.0kg?}\\$

$(a) \; 0.138 \\$
$(b)\; 0.428 \\$
$(c)\; 0.766 \\$
$(d)\; 0.262$

$Ans:\;(a) \; 0.138 \\$

$\text{23. Monthly expenditure on their credit cards, by credit card holders from}\\$
$\text{ a certain bank, follows a normal distribution with a mean of Rs.1,295.00}\\$
$\text{and a standard deviation of Rs.750.00. What proportion of credit card}\\$
$\text{holders spend more than `1,500.00 on their credit cards per month?}\\$

$(a) \; 0.487\\$
$(b)\; 0.392 \\$
$(c)\; 0.500 \\$
$(d)\;0.791$

$Ans: \;(b)\; 0.392 \\$

$\text{24. Let z be a standard normal variable. If the area to the right of z }\\$
$\text{is 0.8413, then the value of z must be:}\\$

$(a) \; 1.00\\$
$(b)\;-1.00 \\$
$(c)\; 0.00\\$
$(d)\; -0.41$

$Ans:\;(b)\;-1.00 \\$

$\text{25. If the area to the left of a value of z (z has a standard normal}\\$
$\text{distribution) is 0.0793, what is the value of z?}\\$

$(a) \;-1.41 \\$
$(b)\; 1.41\\$
$(c)\;-2.25 \\$
$(d)\;2.25$

$Ans:\;(a) \;-1.41 \\$

$\text{26. If }\; P(Z > z) = 0.8508\; \text{what is the value of z (z has a}? \\$
$\text{standard normal distribution)}? \\$

$(a) \; -0.48 \\$
$(b)\; 0.48 \\$
$(c)\;-1.04 \\$
$(d)\;1.04$

$Ans:\;(c)\;-1.04 \\$

$\text{27. If }\; P(Z > z) = 0.5832 \; what is the value of z (z has a } \\$

*** QuickLaTeX cannot compile formula:
\text{ standard normal distribution)?\\

*** Error message:
File ended while scanning use of \text@.
Emergency stop.

$(a) \; -0.48 \\$
$(b)\; 0.48 \\$
$(c)\; 1.04 \\$
$(d)\;-0.21$

$Ans:\; (d)\;-0.21 \\$

$\text{28. In a binomial distribution, the probability of success is twice as }\\$
$\text{that of failure. Then out of 4 trials, the probability of no success is}\\$

$(a) \; \frac{16}{81}\\$
$(b)\; \frac{1}{16}\\$
$(c)\; \frac{2}{27}\\$
$(d)\; \frac{1}{81}$

$Ans:\; (d)\; \frac{1}{81}\\$

Probability Distributions Exercise 7.4

Probability Distributions Exercise 7.4

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