Q: Given a binomial experiment with $$n = 16$$ and $$p = 0.86$$, what is the mean number of successful kidney transplant surgeries?

$$n \times p = 16 \times 0.86 = 13.76$$

Q: On a dry surface, the braking distance of a sedan is normally distributed with mean $$132 ft $$and standard deviation $$4.53 ft. $$What braking distance is the cutoff for the bottom $$20\%$$?

$$132 + (-0.84) \times 4.53 = 128.19 ft$$

Q: Find the standard deviation of the number of successful kidney transplant surgeries in 16 patients, given the probability of success is $$0.86.$$

$$\sqrt{n \times p \times (1-p)} = \sqrt{16 \times 0.86 \times 0.14} \approx 1.40$$

Q: If the probability distribution for the number of cats owned is as follows: $$P(0) = 0.27$$, $$P(1) = 0.47$$, $$P(2) = 0.12$$, $$P(3) = 0.09$$, $$P(4) = 0.05$$, what is the expected (mean) number of cats owned?

$$0 \times 0.27 + 1 \times 0.47 + 2 \times 0.12 + 3 \times 0.09 + 4 \times 0.05 = 1.18$$

Question 1

A probability distribution for the number of cats owned by a person is given as follows: $$P(0) = 0.27$$, $$P(1) = 0.47$$, $$P(2) = 0.12$$, $$P(3) = 0.09$$, $$P(4) = 0.05. $$What is the probability that a randomly selected person owns between 1 and 3 cats, inclusive?

Accepted Answer

$$0.47 + 0.12 + 0.09 = 0.68$$

Question 2

Given a binomial experiment with $$n = 16$$ and $$p = 0.86$$, what is the mean number of successful kidney transplant surgeries?

Accepted Answer

$$n 	imes p = 16 	imes 0.86 = 13.76$$

Question 3

For a standard normal curve, what is the area to the right of $$z = -1.68$$?

Accepted Answer

$$1 - 0.0465 = 0.9535$$

Question 4

IQ scores are normally distributed with mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the probability that a randomly selected person has an IQ higher than 125?

Accepted Answer

$$P(Z \u003e \frac{125-100}{15}) = P(Z \u003e 1.67) = 1 - 0.9525 = 0.0475$$

Question 5

Suppose the yearly black carbon emissions from cars in India are normally distributed with mean $$\mu = 14.7$$ gigagrams and standard deviation $$\sigma = 11.5$$ gigagrams. What is the probability that a randomly selected year has emissions less than 12.3 gigagrams?

Accepted Answer

$$P(Z \u003c \frac{12.3 - 14.7}{11.5}) = P(Z \u003c -0.21) = 0.4168$$

Question 6

For a standard normal curve, what is the area between $$z = 0.51$$ and $$z = 2.68$$?

Accepted Answer

$$P(0.51 \u003c Z \u003c 2.68) = P(Z \u003c 2.68) - P(Z \u003c 0.51) = 0.9963 - 0.6950 = 0.3013$$

Question 7

A discrete probability distribution is valid if which of the following conditions are met?

Accepted Answer

All probabilities are between $$0$$ and $$1$$, and the sum of all probabilities is $$1$$

Question 8

For a standard normal curve, what is the $$z-$$score that corresponds to the $$46th $$percentile?

Accepted Answer

$$z \approx -0.10$$

Question 9

On a dry surface, the braking distance of a sedan is normally distributed with mean $$132 ft $$and standard deviation $$4.53 ft. $$What braking distance is the cutoff for the bottom $$20\%$$?

Accepted Answer

$$132 + (-0.84) 	imes 4.53 = 128.19 ft$$

Question 10

Which of the following justifies that the number of successful kidney transplant surgeries in 16 patients is a binomial random variable?

Accepted Answer

There are a fixed number of trials, each trial is independent, each trial has two outcomes (success/failure), the probability of success is constant, and the random variable counts the number of successes.

Question 11

Find the standard deviation of the number of successful kidney transplant surgeries in 16 patients, given the probability of success is $$0.86.$$

Accepted Answer

$$\sqrt{n 	imes p 	imes (1-p)} = \sqrt{16 	imes 0.86 	imes 0.14} \approx 1.40$$

Question 12

For a standard normal curve, what is the area to the left of $$z = 0.33$$?

Accepted Answer

$$0.6293$$

Question 13

If the probability distribution for the number of cats owned is as follows: $$P(0) = 0.27$$, $$P(1) = 0.47$$, $$P(2) = 0.12$$, $$P(3) = 0.09$$, $$P(4) = 0.05$$, what is the expected (mean) number of cats owned?

Accepted Answer

$$0 	imes 0.27 + 1 	imes 0.47 + 2 	imes 0.12 + 3 	imes 0.09 + 4 	imes 0.05 = 1.18$$

Question 14

For a standard normal curve, what is the $$z-$$score that has $$30.5\%$$ area to the right?

Accepted Answer

$$z \approx 0.51$$

Question 15

Yearly black carbon emissions from cars in India are normally distributed with mean $$14.7$$ and standard deviation $$11.5. $$What is the probability that emissions are between $$15.4$$ and $$19.6$$ gigagrams in a randomly selected year?

Accepted Answer

$$P(15.4 \u003c X \u003c 19.6) = P(Z \u003c 0.43) - P(Z \u003c 0.06) = 0.6664 - 0.5239 = 0.1425$$

Question 16

IQ scores are normally distributed with mean $$100$$ and standard deviation $$15. $$What is the lowest score that would still place a person in the top $$5\% of $$scores?

Accepted Answer

$$100 + 1.645 	imes 15 = 124.68$$

Question 17

For a standard normal curve, what is the area to the right of $$z = -0.57$$?

Accepted Answer

$$1 - 0.2843 = 0.7157$$

Question 18

On a dry surface, the braking distance of a sedan is normally distributed with mean $$132 ft $$and standard deviation $$4.53 ft. $$What braking distance is the cutoff for the top $$15\%$$?

Accepted Answer

$$132 + 1.04 	imes 4.53 = 136.71 ft$$

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