Math Answers

Brenda can deliver 644 newspapers in 7 hours.

How many newspapers can Brenda deliver in 9 hours?

In how many different ways can 3 elements be selected in order from a set with five 10 when repetition is allowed?

5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1

is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly

selected students and derive the probability function for X.

6. A man has four keys in his pocket and, since it is dark, cannot see which

is his door key. He will try each key in turn until he finds the right one.

Let X be the number of keys tried (including the right one) to open the

door. What is the probability function for X?

7. Suppose a fair die is tossed two times. Let X be the larger of the two

faces that appear. Find _px(k).

8. Suppose a particle moves along the x-axis beginning at 0. It moves one

integer step to the left or right with equal probability. What is the probability

function of its position after four steps?

9. Five cards are dealt from a standard 52-card deck. Let Y be the number

of red cards that are dealt. What is the probability function for Y ?

22. For a chi-square distribution,find x²_\alpha

such that

a) P(X² > x²_\alpha) = 0:99 when df = 4;

b) P(X² > x²_\alpha) = 0:025 when df = 19;

c) P(37.652 < X² < x²_\alpha) = 0:045 when df = 25.

23. Find

a) t_0.025 when df = 14

b) -t_0.10 when df = 10

c) t_0.995 when df = 7.

24. Find

a) P(T < 2:365) when df = 7;

b) P(-1.356 < T < 2.179) when df = 12;

c) P(T > 1.318) when df = 24;

d) P(T > -2.567) when df = 17.

25. For an F-distribution, find the value of f such that

a) P(F > f) = 0:05 when df₁ = 4 and df₂ = 9;

b) P(F > f) = 0:05 when df₁ = 9 and df₂ = 4;

c) P(F < f) = 0:95 when df₁ = 5 and df₂ = 8;

d) P(f₁ < F < f₂) = 0:90 when df₁ = 3 and df₂ = 9.

18. The lengths of fully-grown scorpions of a certain variety have a mean of 1.96 inches and standard deviation of 0.08 inch. Assuming that the distribution of these lengths has roughly the shape of a normal distribution, find what percentage of these scorpions have a length of

a) 2.20 inches or more;

b) at least 1.80 inches.

19. With reference to Exercise 18, above what value would we find the longest 6 percent of these scorpions?

20. The distribution of the IQ's of the 4,000 employees of a large company has a mean of 104.5, a standard deviation of 13.9, and its shape is roughly that of a normal distribution. Given that a certain job requires a minimum IQ of 95 and bores those with an IQ over 110, how many of the company's employees are suitable for this job on the basis of IQ alone?

21. For a chi-square distribution, find

a) x²_0.025 when df = 15;

b) x²_0.01 when df = 7;

c) x²_0.05 when df = 24

15. The grapefruits grown in a large orchard have a mean weight of 18.2 ounces with a standard deviation of 1.2 ounces. weights of these grapefruits has roughly the shape of a normal distribution, what percentage of the grapefruit weigh

a) less than 16.1 ounces;

b) more than 17.3 ounces;

c) anywhere from 16.7 to 18.8 ounces?

16. With reference to Exercise 15, find

a) the weight above which we will find the heaviest 15% and 75% of the grapefruits;

17. A manufacturer needs coil springs that can stand a load of at least 20.0 pounds. Among two suppliers, Supplier A can supply coil springs that, on the average, can stand a load of 24.5 pounds with a standard deviation of 2.1 pounds, and Supplier B can supply coil springs that, on the average, can stand a load of 23.3 pounds with a standard deviation of 1.6 pounds. distributions of these loads can be apprx with a normal distributions, determine which of the two suppliers can provide the manufacturer with the smaller percentage of unsatisfactory coil springs.

11. Find z if the standard normal-curve area

a) between 0 and z is 0.4726;

b) to the left of z is 0.9868;

c) to the left of z is 0.3085;

d) between -z and z is 0.9282

12. If a random variable has the normal distribution with \mu = 82:0 and
\sigma = 4:8, nd the probabilities that it will take on a value

a) less than 89.2;

b) greater than 78.4;

c) between 83.2 and 88.0;

d) between 73.6 and 90.4.

13. If the time to assemble an \easy to assemble" computer desk from a

kit is a random variable having the normal distribution with \mu = 55:8
minutes and \sigma = 12:2 minutes, what are the probabilities that this

kind of desk can be assembled in

a) less than 49.7 minutes;

b) anywhere from 61.9 and 74.1 minutes;

c) more than 86.3 minutes?

14. With reference to Exercise 13, for what length of time is the probability

0.90 that one can assemble the desk in that many minutes or less?

8. A quality control engineer wants to check whether, in accordance with specication, 90% of products shipped are in perfect working condition. To this end, she randomly selects 12 items from each lot ready to be shipped and passes the lot only if all 12 are in perfect working condition. If one or more are not in perfect working condition, she holds the lot for a complete inspection. Find the probability that she will commit the error of

a) holding a lot for a complete inspection even though 90% of the items are in perfect working condition;

b) letting a lot pass through even though only 80% of the items are in perfect working condition;

10. Find the area under the standard normal curve that lies

a) between z = 0 and z = 0.87;

b) between z = -1.66 and z = 0;

c) to the right of z = 0.48;

d) to the right of z = -0.27;

e) to the left of z = 1.30;

f) between z = 0.45 and z = 1.23;

h) between z = 1.15 and z = 1.23;

i) between z = -1.35 and z = 1.35

j) between z = -2.35 and z = -1.46.

4. Explain in each case why the given equation cannot serve as the probability density function of a random variable that takes on values on the interval from 0 to 5:

a) f(x) = 1/10 (x - 4);

b) f(x) = 1/50 (x + 1).

5. A doctor knows from experience that 10% of of the patients to whom

he prescribes a certain blood pressure medication will have undesirable

side effects. Calculate the probability that of the 10 randomly selected

patients:

a) none will have undesirable side effects;

b) exactly 4 patients will have undesirable side effects;

c) at most 3 will have undesirable side effects;

d) at least 3 will have undesirable side effects.

6. Refer to Exercise 5. What is the expected number of patients with

undesirable side effects. What is the standard deviation of the number

of patients with undesirable side effects.

The first term of a geometric series is 9 and the ratio of the sum of the first eight terms to the sum of the first four terms is 97:81.

Calculate the first 3 terms of the sequence it is given that all the terms are positive.