Q: Given the same probability distribution for the number of busy telephone lines, what is the expected (mean) number of busy lines?

$$E[X] = 0 \times 0.1 + 1 \times 0.2 + 2 \times 0.4 + 3 \times 0.3 = 1.9$$

Q: For the same weather person, what is the mean number of days she is accurate in 5 days?

$$\mu = n p = 5 \times 0.8 = 4$$

Q: SAT scores are normally distributed with mean $$\mu = 1643$$ and standard deviation $$\sigma = 341.3. $$According to the empirical rule, what is the range of scores that covers approximately 95% of the data?

$$1643 \pm 2 \times 341.3 = (960.4, 2325.6)$$

Q: A random sample of 100 pocket calculators has a mean life of 21 months and sample standard deviation of 2.8 months. What is the 95% confidence interval for the mean life expectancy?

$$21 \pm 1.96 \times \frac{2.8}{\sqrt{100}} = (20.45, 21.55)$$

Question 1

An accountant has 3 incoming telephone lines. The probability distribution for the number of busy lines $$X is$$: $$P(X=0)=0.1$$, $$P(X=1)=0.2$$, $$P(X=2)=0.4$$, $$P(X=3)=0.3. $$What is the probability that fewer than 2 lines are busy?

Accepted Answer

$$0.1 + 0.2 = 0.3$$

Question 2

Given the same probability distribution for the number of busy telephone lines, what is the expected (mean) number of busy lines?

Accepted Answer

$$E[X] = 0 	imes 0.1 + 1 	imes 0.2 + 2 	imes 0.4 + 3 	imes 0.3 = 1.9$$

Question 3

A weather person is accurate within 2 degrees 80% of the time. What is the probability she is accurate exactly 3 out of the next 5 days?

Accepted Answer

$$P = \binom{5}{3} (0.8)^3$ (0.2)^2$ = 0.2048$$

Question 4

For the same weather person, what is the mean number of days she is accurate in 5 days?

Accepted Answer

$$\mu = n p = 5 	imes 0.8 = 4$$

Question 5

The lengths of long distance calls from a city are normally distributed with mean $$\mu = 10$$ minutes and standard deviation $$\sigma = 3$$ minutes. What is the probability that a randomly selected call lasts more than 16 minutes?

Accepted Answer

$$P(X \u003e 16) = P\left(Z \u003e \frac{16-10}{3}\right) = P(Z \u003e 2) = 0.0228$$

Question 6

SAT scores are normally distributed with mean $$\mu = 1643$$ and standard deviation $$\sigma = 341.3. $$According to the empirical rule, what is the range of scores that covers approximately 95% of the data?

Accepted Answer

$$1643 \pm 2 	imes 341.3 = (960.4, 2325.6)$$

Question 7

A sample of 64 teacher salaries has a mean of $$56,300$$ and population standard deviation $$7,200. $$What is the probability that the sample mean is within $$1,000 of $$the population mean?

Accepted Answer

$$P = P\left(\left|\overline{X} - 56,300\right| \u003c 1,000\right) = P\left(\left|Z\right| \u003c \frac{1,000}{7,200/\sqrt{64}}\right) = P(|Z| \u003c 1.11) = 0.7330$$

Question 8

A random sample of 100 pocket calculators has a mean life of 21 months and sample standard deviation of 2.8 months. What is the 95% confidence interval for the mean life expectancy?

Accepted Answer

$$21 \pm 1.96 	imes \frac{2.8}{\sqrt{100}} = (20.45, 21.55)$$

Question 9

A sample of 10 adult females has a mean iron intake of $$14.10 mg$$, sample standard deviation $$4.2 mg. $$Test at the 1% significance level if the mean is less than the RDA of $$18 mg. $$What is the value of the test statistic?

Accepted Answer

$$t = \frac{14.10 - 18}{4.2/\sqrt{10}} = -2.94$$

Question 10

If the true mean iron intake is 18 mg, but we reject the null hypothesis that $$\mu = 18$$, what type of error have we made?

Accepted Answer

Type I error

Question 11

If the true mean iron intake is less than 18 mg, but we fail to reject the null hypothesis that $$\mu = 18$$, what type of error have we made?

Accepted Answer

Type II error

Question 12

A sample of 100 women in a city has a mean height of 61.1 inches, with sample standard deviation 3.6 inches. The national mean is 62.3 inches. What is the value of the test statistic for testing if the city mean is lower than the national mean?

Accepted Answer

$$z = \frac{61.1 - 62.3}{3.6/\sqrt{100}} = -3.33$$

Question 13

If the actual average height of women in the city is 62.3 inches, but we reject the null hypothesis that $$\mu = 62.3$$, what type of error have we made?

Accepted Answer

Type I error

Question 14

If the actual average height of women in the city is 61 inches, but we fail to reject the null hypothesis that $$\mu = 62.3$$, what type of error have we made?

Accepted Answer

Type II error

Question 15

Given the data set: 77, 70, 72, 66, 75, which of the following is NOT a method to assess normality of the data?

Accepted Answer

Calculating the mean and standard deviation only

Question 16

A normal probability plot of a data set is approximately linear. What does this suggest about the data?

Accepted Answer

The data are approximately normally distributed

Question 17

A boxplot of a data set shows a long whisker on the right side. What does this indicate?

Accepted Answer

The data are skewed to the right

Question 18

If a hypothesis test is conducted at the 5% significance level, what is the probability of making a Type I error?

Accepted Answer

$$0.05$$

Question 19

Which of the following best describes the standard deviation of a binomial distribution with parameters $$n$$ and $$p$$?

Accepted Answer

$$\sigma = \sqrt{n p (1-p)}$$

Final Exam Review Guidance for MAT 124 (Statistics) Chapters 6–10

Guida di studio - Domande di pratica

Study guide - Flashcard