What is the probability that the random variable has a value between 0.3 and 0.7?

If Z is a standard normal variable, find the probability.

The probability that Z is greater than -1.82

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.

If 9% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

Solve the problem.

Assume that X has a normal distribution with mean 5 and standard deviation 2. Find the indicated probability.

P(3 < X < 7)

Find the indicated probability.

In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.

Solve the problem.

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. In a random sample of 9000, approximately how many people will have IQs between 85 and 120?

Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%.

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 140 mm Hg and a standard deviation of 12.2 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 90% of all blood pressures are between them.

The scores on a certain test are normally distributed with a mean score of 70 and a standard deviation of 3. What is the probability that a sample of 90 students will have a mean score of at least 70.3162?

A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 76.

For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 36 women are selected at random from a population of 300 women aged 18-24, find the probability that their mean systolic blood pressure will be less than 110 mm Hg. Assume that the sampling is done without replacement and use a finite population correction factor with N = 300.

Use the continuity correction and describe the region of the normal curve that corresponds to the indicated binomial probability.

The probability that the number of correct answers is between 27 and 49 inclusive

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation.

n = 19 and p = .2

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Use the normal distribution to approximate the desired probability.

A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 16 tosses. What is the probability of being correct 16 or more times by guessing? Does this probability seem to verify her claim?

Solve the problem.

An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%?

Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct.

Solve the problem.

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-a < z < a) = 0.4314, find a.