Applications with Standard Normal Distribution Answers

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.zProbability0.000.50000.500.69151.000.84132.000.97723.000.9987

For a standard normal distribution, if , what is the value of ?

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.220.58710.320.62550.420.66280.440.67000.640.73890.840.79951.000.8413

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 Probability0.000.50001.000.84132.000.97723.000.9987

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

For a standard normal distribution, which of the following variables always equals 1?

The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to –z standard deviations from the mean?

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59871.000.84131.250.89441.500.93321.750.9599

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

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.zProbability0.000.50001.000.84132.000.97723.000.9987