# Question

A survey asked recently retired people the number of people, X, they met through work during their working lives that they considered close friends. The table below is a probability distribution table representing the data collected. Find the mean and the standard deviation of the probability distribution using Excel.

Round the mean and standard deviation to three decimal places.

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**Question**

A study randomly selected 100 samples, each of which consisted of 100 people, and recorded the number of left-handed people, X. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.

- Round the mean and standard deviation to two decimal places.

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**Question**

Connor is a statistics student interested in the number of games won by each team per season during the past 12 years for a certain professional baseball league. He records the total number of wins x for each team each season and the probability of each value P(x), as shown in the table provided. Use Excel to find the mean and the standard deviation of the probability distribution.

- Round the mean and standard deviation to three decimal places.

**Question**

An insurance office records the number of claims received each day, X, and built the probability distribution table below using the data collected. Find the mean and the standard deviation of the probability distribution using Excel.

- Round the mean and standard deviation to two decimal places.

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**Question**

Isaac, a manager at a supermarket, is inspecting cans of pasta to make sure that the cans are not dented and do not have other defects. From past experience, he knows that 1 can in every 80 is defective. What is the probability that Isaac will find his first defective can among the first 45 cans? Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

Katie handles calls for a company’s information technology help desk, either by resolving the issue herself or forwarding the call to the appropriate team. About 12.9% of the help desk calls need to be forwarded to another team. What is the probability that the first call Katie needs to forward to another team will be one of the first seven calls she receives that day? Use Excel to find the probability.

- Round your answer to three decimal places.

# Question

An insurance company is assessing the risk of selling flood insurance. Under the company’s policies, if a customer lives in an area where they have a greater than 5% chance of experiencing 4 or more floods in 10 years, the customer must pay a higher premium. Drew lives in an area where the average number of floods per 10 years is 1.6 floods. Will Drew have to pay the higher premium for flood insurance? Use Excel to find the probability.

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# Question

In a 40-year period, a city’s official weather station recorded 78 snowstorms with at least 12 inches of total snow accumulation. Assume that this pattern follows a Poisson distribution. Find the probability that the city’s weather station records exactly 4 snowstorms with at least 12 inches of total snow accumulation for one randomly selected year in the period. Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

At a certain fast food restaurant, 77.5% of the customers order items from the value menu. If 14 customers are randomly selected, what is the probability that at least 9 customers ordered an item from the value menu? Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

A roulette wheel has 38 slots, numbered 1 to 36, with two additional green slots labeled 0 and 00. Jim, a dealer at a roulette table, tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands. The ball has an equally likely chance of landing in each slot. If Jim spins the ball around the wheel 25 times, what is the probability that the ball lands in a green slot at most twice? Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a letter from A to F. Assume that each number or letter being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

The state department of transportation is coordinating road crews to fix potholes after a particularly snowy winter. Initial estimates gave an average of 7.8 potholes per mile of highway. Find the probability that there are 11 or more potholes in a randomly selected one-mile stretch of highway. Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

A roulette wheel has 38 slots, numbered 1 to 36, with 2 additional green pockets labeled 0 and 00. Jim, a dealer at a roulette table, tests the roulette wheel by spinning a ball around the wheel repeatedly and seeing where the ball lands. What is the probability that Jim will spin the wheel at most 11 times before landing a ball in one of the green pockets? Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

In a recent baseball season, Ron was hit by pitches 21 times in 602 plate appearances during the regular season. Assume that the probability that Ron gets hit by a pitch is the same in the playoffs as it is during the regular season. In the first playoff series, Ron has 23 plate appearances. What is the probability that Ron will get hit by a pitch exactly once? Use Excel to find the probability.

- Round your answer to three decimal places.

**Question**

If a fair coin is tossed 25 times, the probability distribution for the number of heads, X, is given below. Find the mean and the standard deviation of the probability distribution using Excel.

- Enter the mean and round the standard deviation to two decimal places.

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# Question

An automobile manufacturer is concerned about the possibility of a fault in the engine of a particular model of one of its cars. This fault could potentially cause the engine to fail to start. The average number of cars per year that experience this fault is 3 cars. If the probability that 8 or more cars experience this fault in a year is greater than 0.05, the company will issue a recall. Will the company issue a recall for this engine fault? Use Excel to find the probability.

**Question**

To see if a spinner that is divided into 100 equal sections labeled 1 to 100 is fair, a researcher spins the spinner 1000 times and records the result. Let X represent the outcome. The table below shows the probability distribution of the data. Find the mean and the standard deviation of the probability distribution using Excel.

- Round the mean and standard deviation to two decimal places.

# Question

Burt, a football quarterback, has a pass completion percentage of 55.2%. If the probability that Burt will need 8 or more pass attempts to complete his first pass in a game is at least 0.01, then Burt will be benched and replaced by a backup. Will Burt be benched? Use Excel to find the probability, rounding to three decimal places.

**Solution:**

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