1. For each term, identify the number of trials the probability p of success the number of successes (} 10 7 b) (} 8 3 2. A class has eight students. What is the probability that exactly four of the students were born on a weekday (Monday through Friday)? 3. A hotel has four elevators One of them is a freight elevator. When pressing the button, one of the elevators randomly serves your floor.If you use the elevators seven times, what is the probability that you use the freight elevator exactly three times? . A game is played with a spinner on a circle, like the minute hand on a clock The circle is marked evenly from 1 to 90 The player spins the spinner and the resulting number is the number of seconds the player is given to solve a randomly selected mathematics problem. Suppose there are 30 students playing in the class a) What is the probability that 10 of the students received over a minute to solve the problem? b) What is the probability that exactly half of the students received 30 or less seconds? c) What is the probability that the four to tell iconve more than aminute? d) What is the probability thefage a. If ofthe students indeivetu seconds or more?

Question

1. For each term, identify the number of trials the probability p of success the number of successes (} 10 7 b) (} 8 3 2. A class has eight students. What is the probability that exactly four of the students were born on a weekday (Monday through Friday)? 3. A hotel has four elevators One of them is a freight elevator. When pressing the button, one of the elevators randomly serves your floor.If you use the elevators seven times, what is the probability that you use the freight elevator exactly three times? . A game is played with a spinner on a circle, like the minute hand on a clock The circle is marked evenly from 1 to 90 The player spins the spinner and the resulting number is the number of seconds the player is given to solve a randomly selected mathematics problem. Suppose there are 30 students playing in the class a) What is the probability that 10 of the students received over a minute to solve the problem? b) What is the probability that exactly half of the students received 30 or less seconds? c) What is the probability that the four to tell iconve more than aminute? d) What is the probability thefage a. If ofthe students indeivetu seconds or more?

Answer 1

### 1a) n=10, p=3/4, k=7### 1b) n=8, p=1/3, k=3### 2) 0.243### 3) 0.173### 4a) 0.153### 4b) 0.014### 4c) 0.012### 4d) 0.572

Answer 2

## Step 1: Identifying Binomial Distribution Parameters### For each term, identify the number of trials (n), the probability of success (p), and the number of successes (k).* **a)

**:

,

* **b)

**:

,

## Step 2: Probability of Weekday Birthdays### Calculate the probability of exactly four students being born on a weekday.The probability of being born on a weekday is

. We have 8 students and want exactly 4 born on a weekday. This is a binomial probability:

## Step 3: Freight Elevator Probability### Calculate the probability of using the freight elevator exactly three times out of seven.The probability of using the freight elevator is

. We use the elevator 7 times and want exactly 3 uses of the freight elevator. This is a binomial probability:

## Step 4: Spinner Game Probabilities### Calculate the probabilities for the spinner game scenarios.* **a) Probability of 10 students receiving over a minute:** The probability of getting over a minute (more than 60 seconds) is

. With 30 students, we want exactly 10 with over a minute:

* **b) Probability of exactly half receiving 30 seconds or less:** The probability of 30 seconds or less is

. We want exactly half (15) of the 30 students to have this outcome:

* **c) Probability of the first four receiving over a minute:** The probability of over a minute is

. We want all four to have this outcome:

* **d) Probability of at least 15 receiving 45 seconds or more:** The probability of 45 seconds or more is

. We want at least 15 students to have this outcome. This involves summing the probabilities from 15 to 30 successes:

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