Math Answers

Consider the design of a communication system.

⦁ How many three-digit phone prefixes that are used to represent a particular geographic area (such as an area code) can be created from the digits 0 through 9?

⦁ As in part i., how many three-digit phone prefixes are possible that do not start with 0 or 1, but contain 0 or 1 as the middle digit?

⦁ How many three-digit phone prefixes are possible in which no digit appears more than once in each prefix?

Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries.

⦁ How many different sequences are possible?

⦁ How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively?

⦁ How many different schedules begin and end with a knee surgery?

Number plates in an Arab country consist of 3 letters (chosen from a specified set of 20 letters from the Arabic alphabet) and 4 digits (from 0 to 9).

⦁ Find the probability of a plate having identical letters.

⦁ Find the probability of a plate having identical digits.

⦁ Find the probability of a plate having consecutive digits.

Consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What percentage of IQs are

a. greater than 95?

b. less than 120

c. between 90 and 110

Determine whether (p ∧ (p → q)) →q is a tautology using laws of logic.

Determine whether (¬q ∧ (p → q)) → ¬p) is a tautology using laws of logic.

What's More

Let's see how well you understood our discussion. At this point, I want you to

solve the following problems. Show your complete solution by following the step-by-

step procedure.

1. The average number of milligrams (mg) of cholesterol in a cup of a certain brand

of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is

normally distributed.

a. If a cup of ice cream is selected, what is the probability that the cholesterol

content will be more than 670 mg?

b. If a sample of 10 cups of ice cream is selected, what is the probability that

the mean of the sample will be larger than 670 mg?

2. In a study of the life expectancy of 400 people in a certain geographic region, the

mean age at death was 70 years, and the standard deviation was 5.1 years. If a

sample of 50 people from this region is selected, what is the probability that the

mean life expectancy will be less than 68 years?

2 A tunnelling machine drills 500 metres. Use your values from the

table to estimate the cost of drilling if the first metre costs £X and

each extra met

re costs £Y.

x=17

y=272

"An electrical firm produces light bulbs that have a length of life that is approximately normally distributed with a mean of 680 hours and a population standard deviation of 26 hours. A new version of light bulbs is being produced and is assumed to be better than the previous version. To test this claim, a random sample of 93 new light bulbs are tested. Would you agree with this claim if the random sample showed an average of 920 hours? Use a 0.1 level of significance.

What are the given? Write only the number. :

population mean: Blank 1 hours

population standard deviation: Blank 2 hours

sample size: Blank 3

sample mean: Blank 4 hours

level of significance: Blank 5

What is the critical value?

z: Blank 6

What is the value of the calculated z? Round your answer to the nearest hundredths.

z: Blank 7"

let x be a binomial random variable. use the formula to compute the following probabilities;

(a) p(x=2), if n=8 and p=0.1

(b) p(x=5), if n=9 and p=0.5

(c) p(x=9), if n=10 and p=0.95