Question 1

An event with a probability of $$\frac{11}{20} is $$considered unusual. Is this statement true or false?

Accepted Answer

False

Question 2

In a study on the prevalence of a rare condition, the following probability distribution was found for the number of patients $$y ($$out of 6) who reported the condition:

$$\begin{array}{c|ccccccc}
y & 0 & 1 & 2 & 3 & 4 & 5 & 6 \
P(Y=y) & 0.160 & 0.330 & 0.275 & 0.145 & 0.065 & 0.020 & 0.005 \
\end{array}$$

Find the probability that at least 1 of the 6 patients has the condition.

Accepted Answer

0.840

Question 3

A health clinic conducted a 'Rapid Flu' test:
- 135 individuals tested positive, 22 were false positives.
- 165 individuals tested negative, 4 were false negatives.

If one test participant is randomly selected, what is the probability that they did NOT have the flu or tested positive?

Accepted Answer

0.9267

Question 4

A survey of high school students on screen habits and sleep patterns produced the following table:

$$\begin{array}{l|cc}
 & 	ext{Reported Poor Sleep} & 	ext{Did Not Report Poor Sleep} \
\hline
	ext{Used Electronic Devices Before Bed} & 800 & 2940 \
	ext{Did Not Use Electronic Devices Before Bed} & 210 & 4030 \
\end{array}

If $$one student is randomly selected, what is the probability that the student did NOT use electronic devices before bed and did NOT report poor sleep?

Accepted Answer

0.39375

Question 5

A college tracks the number of male and female students who graduate with degrees in science and non-science fields:

$$\begin{array}{l|cc}
 & 	ext{Science} & 	ext{Non-Science} \
\hline
	ext{Male} & 75{,}000 & 105{,}000 \
	ext{Female} & 95{,}000 & 125{,}000 \
\end{array}$$

What is the probability that a randomly selected science graduate is male?

Accepted Answer

0.441

Question 6

In a group of 8 students, 4 are left-handed. If 3 students are selected at random without replacement, what is the probability that all three are left-handed?

Accepted Answer

0.0714

Question 7

Let $$P(G) = 0.5$$, $$P(\overline{G}) = 0.5$$, $$P(H|G) = 0.4$$, and $$P(H|\overline{G}) = 0.1. $$What is $$P(G|H)$$ according to Bayes' Theorem?

Accepted Answer

$$\frac{4}{11}$$

Question 8

A jar contains 10 marbles numbered 1 through 10. Event D is drawing the marble numbered 7. How many outcomes are in Event D, and is it a simple event?

Accepted Answer

1: Yes

Question 9

A phone number (excluding the area code) consists of seven digits in a specific order, and digits may repeat. Suppose you already know the last three digits of a person's phone number from a form they filled out. If you randomly guess the remaining four digits, what is the probability that you correctly guess the entire phone number?

Accepted Answer

0.0001

Question 10

A company's average monthly electricity bill is $$320. Due to a rate change, each bill is increased by 7% and a fixed service charge of 25 is $$added. What is the new mean monthly bill?

Accepted Answer

$345.00

Question 11

62% of employees prefer email as their primary method of workplace communication. You randomly select 10 employees and ask whether they prefer email. The random variable $$X$$ represents the number of employees who prefer email.

(i) What is the most appropriate description of the histogram's shape?
(ii) Which value of $$X$$ would be considered unusual?
(iii) Why is this value considered unusual?

Accepted Answer

i. Shape: skewed left
 ii. $$X=2$$
 iii. because it has a probability less than 0.05

Question 12

A call center receives an average of 3.2 calls per hour. Assuming the number of calls follows a Poisson distribution, what is the probability that in a randomly selected hour, the call center receives exactly 3 calls?

Use the Poisson formula: $$P(X=k) = \frac{\lambda^k e$$^{-\lambda}$$}{k!}$$ where $$\lambda=3.2$$, $$k=3.$$

Accepted Answer

0.2230

Question 13

A shipment contains 7,500 bolts, with 18% classified as substandard. If a supervisor randomly selects 6 bolts for testing, what is the probability that none of the selected bolts are substandard? Selections are made without replacement.

Accepted Answer

0.304

Question 14

A random variable $$W is $$normally distributed with a mean of 120 and a standard deviation of 20. Find $$P(W \u003e 100).$$

Accepted Answer

0.8157

Question 15

Suppose the daily amount of nitrogen dioxide in a city is normally distributed with a mean of 18.6 parts per billion and a standard deviation of 5.1 parts per billion. What is the probability that on a randomly selected day, the nitrogen dioxide level is between 12.0 and 25.0 parts per billion?

Accepted Answer

0.8953

Question 16

The mean daily rainfall in a rainforest region is normally distributed with a mean of 18.2 mm and a standard deviation of 6.3 mm. If a sample of 10 days is randomly chosen, what is the probability that the sample mean rainfall is greater than 22.8 mm?

Accepted Answer

0.0051

Question 17

A research team wants to estimate the standard deviation of time spent on social media by teenagers. Find the minimum sample size needed to be 99% confident that the sample standard deviation $$S is $$within 3% of the population standard deviation $$\sigma.$$

Accepted Answer

7373

Question 18

A researcher collects the following weights in grams of dimes minted after 2000: 2.312, 2.284, 2.298, 2.315, 2.289, 2.301, 2.307, 2.294, 2.319, 2.288. Construct a 95% confidence interval estimate of the mean weight of all dimes minted after 2000. The official specification requires a weight of 2.268 grams. Does the confidence interval suggest the mean meets the specification?

Accepted Answer

(2.292 grams, 2.309 grams), the confidence interval suggests the mean meets the specification

Statistics Study Guide: Probability, Distributions, and Statistical Inference

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