Answers LAUSD-Algebra II B Prescriptive - SummerIntroduction to Normal Distributions

Applications with Standard Normal Distribution Answers

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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?

0.16

0.4

2.5

6.25

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

0.2116

0.2884

0.7116

0.7884

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

11%

39%

61%

89%

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. zProbability0.000.50001.000.84132.000.97723.000.9987

0.02

0.14

0.34

0.84

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

47.5%

68%

95%

99.7%

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

16%

34%

66%

84%

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.zProbability0.000.50000.250.59870.500.69150.750.77341.000.84131.250.89441.500.93321.750.9599

P (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.25)

P (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.75)

P (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25)

P (0.75 less-than-or-equal-to z less-than-or-equal-to 1.25)

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

0.16

0.68

0.82

0.84

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?

The probability is less than p%.

The probability is equal to p%.

The probability is greater than p%.

The probability is not equal to p%.

Which of the following statements is equivalent to ?