The Normal Distribution

According to the introduction of Chapter 6, the normal probability density function is most important for which reason?

What are the two parameters that define a normal distribution?

What is the key characteristic of the Standard Normal Distribution?

What does a z-score measure?

According to the Empirical Rule, what percentage of values in a normal distribution lie within two standard deviations of the mean?

Final exam scores in a statistics class were normally distributed with a mean of 63 and a standard deviation of five. What is the z-score for a student who scored 65?

The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three. What is the probability that a randomly selected golfer scored less than 65?

In a normal distribution, if the area to the left of x is 0.123, what is the area to the right of x?

What is a primary reason for standardizing a normal distribution to a standard normal distribution?

Under what condition can the normal distribution be used to approximate the binomial distribution?

The life of a wearable fitness device is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. What is the probability that a device will last between 2.8 and 6 years?

An experiment with a probability of success given as 0.40 is repeated 100 times. Using the normal distribution to approximate the binomial, what is the probability the experiment will have at least 45 successes?

A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?

Suppose X ~ N(–3, 1). Between what x values does 95.45 percent of the data lie?

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the z-score for a patient who takes ten days to recover?

IQ is normally distributed with a mean of 100 and a standard deviation of 15. What is the minimum IQ needed to qualify for MENSA, an organization for the top 2 percent of all IQs?

If you cannot reject the null hypothesis in a regression analysis, what does this imply about the relationship between the independent and dependent variables?

What is the primary reason that a normal distribution is a poor fit for estimating a binomial distribution when the probability of success (p) is far from 0.5?

The heights of 430 National Basketball Association players were found to be normally distributed with a mean of 79 inches and a standard deviation of 3.89 inches. What is the z-score for a player who is 77 inches tall?

Using the data for NBA players (µ = 79, σ = 3.89), would you believe a player who reported his height had a z-score of 3.5?

In a normal distribution, what percentage of values lie between the first and second standard deviations from the mean (on both sides)?

The length of time to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. What is the probability that it takes at least eight minutes to find a parking space?

Using the parking space scenario (µ = 5, σ = 2), 70 percent of the time, it takes more than how many minutes to find a parking space?

The height for Asian adult males is normally distributed with a mean of 66 inches and a standard deviation of 2.5 inches. What is the probability that a person is between 65 and 69 inches?

For the height of Asian adult males (µ = 66, σ = 2.5), what range of heights represents the middle 40 percent of the data?

A citrus farmer finds the diameters of their mandarin oranges follow a normal distribution with a mean of 5.85 cm and a standard deviation of 0.24 cm. What is the probability that a randomly selected orange has a diameter larger than 6.0 cm?

Using the mandarin orange data (µ=5.85, σ=0.24), what is the 16th percentile for the diameters?

What is the primary visual difference between a normal distribution curve and a Student's t-distribution curve with a small number of degrees of freedom?

An experiment with a probability of success of 0.30 is repeated 90 times. What is the mean (µ) of the corresponding binomial distribution?

An experiment has a probability of success of 0.30 and is repeated 90 times. Can the normal distribution be used to approximate this binomial distribution?

For a standard normal distribution, what is the probability P(Z > 0)?

What is the relationship between P(x < 1) and P(x ≤ 1) for a continuous normal distribution?

A hospital has 49 births in a year. If it is equally likely for a birth to be a boy or a girl, what is the standard deviation for the number of boys?

Can the binomial distribution for 49 births (p=0.5 for a boy) be approximated with a normal distribution?

In a large city, one in ten fire hydrants are in need of repair. If a crew examines 100 fire hydrants, what is the probability they will find nine or fewer that need repair?

On an assembly line, 85 percent of products have no defects. If 50 items are assembled, what is the probability that at least 4 and no more than 8 are defective?

Which of the following is a key reason the normal distribution is used to estimate the hypergeometric distribution?

If a z-score is calculated to be -1.25 for a value x=5, what does this signify?

What is the primary effect of increasing the standard deviation (σ) on the shape of a normal distribution curve, while keeping the mean (µ) constant?

The systolic blood pressure of males is normally distributed with a mean of 125 and a standard deviation of 14. What is the z-score for a blood pressure of 100?

A student takes a 32-question multiple-choice exam and randomly guesses each answer, which has three possible choices. Can this situation be approximated by a normal distribution?

The distance of fly balls is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. What is the probability that a randomly chosen fly ball traveled fewer than 220 feet?

In China, four-year-olds in rural areas average three hours a day unsupervised, with a standard deviation of 1.5 hours. Assuming a normal distribution, what percentage of these children spend over ten hours per day unsupervised?

The duration of a criminal trial is normally distributed with a mean of 21 days and a standard deviation of seven days. Sixty percent of all trials of this type are completed within how many days?

A motorcycle racer averages 129.71 seconds per lap with a standard deviation of 2.28 seconds. What percentage of the racer's laps are completed in less than 130 seconds?

Using the motorcycle racer data (µ=129.71, σ=2.28), the middle 80 percent of the racer's laps are between which two times?

An automotive factory can build an average of 6,000 cars a week, and 10 percent of the cars are defective. In a random sample of 100 cars, what range represents the number of defective cars within one standard deviation of the mean, according to the 68-95-99.7 empirical rule?

On average, 28 percent of 18 to 34 year olds check social media before getting out of bed. Assuming this percentage follows a normal distribution with a standard deviation of 5 percent, what is the probability that the percent of this age group who do so is at least 30 percent?

Using the social media scenario (µ=28, σ=5), what is the 95th percentile for the percent of 18 to 34 year olds who check social media before getting out of bed?

Why must both np and n(1-p) be greater than 5 to use the normal approximation for the binomial distribution?