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?
Explanation
This question applies the normal approximation to the binomial to find a cumulative probability. It requires calculating the mean and standard deviation of the binomial, finding the z-score, and then finding the corresponding left-tail area.
Other questions
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?
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?