Determine whether the statement is true or false:

An event with a probability of $\frac{11}{20}$ is considered unusual.

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

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

Use the following results from the 'Rapid Flu' test conducted by a health clinic.

• Among $135$ individuals who tested positive, $22$ were false positives.
• Among $165$ individuals who tested negative, $4$ were false negatives.

If one of the test participants is randomly selected, find the probability that they did not have the flu or tested positive.

A study on screen habits and sleep patterns collected survey results from high school students aged $16$ and older. The table below summarizes responses based on whether students used electronic devices right before bed and whether they reported poor sleep quality.

If one high school student is randomly selected, find the probability that the selected student did not use electronic devices before bed and did not report poor sleep.

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

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

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

Let $P\left(G\right)=0.5,P\left(G^{\prime }\right)=0.5,P\left(H\mid G\right)=0.4,$ and $P\left(H\mid G^{\prime }\right)=0.1$. What is $P\left(G\mid H\right)$ according to Bayes’ Theorem?

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?

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?

A company’s average monthly electricity bill is $\mathrm{\backslash (}320$. Due to a rate change, each bill is increased by $7\%$ and a fixed service charge of $\mathrm{\backslash )}25$ is added. What is the new mean monthly bill?

$62\%$ of employees prefer email as their primary method of workplace communication. You randomly select $10$ employees and ask whether they prefer email as their primary communication method.

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?

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?

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.

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

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?

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

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 $\sigma$.

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?