applications with standard normal distribution

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.

16%

A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the mean is 25?

2.5

For a standard normal distribution, find the approximate value of mc006-1.jpg. Use the portion of the standard normal table below to help answer the question. z Probability 0.00 0.5000 0.25 0.5987 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599

89%

About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?

95%

Which of the following probabilities is equal to approximately 0.2957? Use the portion of the standard normal table below to help answer the question. z Probability 0.00 0.5000 0.25 0.5987 0.50 0.6915 0.75 0.7734 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599

P(.25 lessthanorequalto z lessthanorequlto 1.25)

If a data value in a normal distribution has a negative z-score, which of the following must be true?

The data value must be less than the mean.

For a standard normal distribution, if mc007-1.jpg, what is the value of mc007-2.jpg?

b

What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. z Probability 0.00 0.5000 1.00 0.8413 2.00 0.9772 3.00 0.9987

.14

What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. z Probability 0.00 0.5000 1.00 0.8413 2.00 0.9772 3.00 0.9987

.18

What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table to help answer the question.z Probability 0.00 0.5000 1.00 0.8413 2.00 0.9772 3.00 0.9987

.81

What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. z Probability 0.00 0.5000 1.00 0.8413 2.00 0.9772 3.00 0.9987

.86

which of the following statements is equivalent to P(z greaterthanorequalto 1.7)

1-P(z greaterthanorequalto -1.7)

For a standard normal distribution, which of the following variables always equals 0?

u