50 70 90 110 100 80 60 (b) What is the probability the random variable will assume a value between 50 and 110? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 70 and 90? (Round your answer to three decimal places.)

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(b) What is the probability the random variable will assume a value between 50 and 110? (Round your answer to three decimal places.)
(c) What is the probability the random variable will assume a value between 70 and 90? (Round your answer to three decimal places.)
Transcribed Image Text:50 70 90 110 100 80 60 (b) What is the probability the random variable will assume a value between 50 and 110? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 70 and 90? (Round your answer to three decimal places.)
A random variable is normally distributed with a mean of u = 80 and a standard deviation of o = 10.
(a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 50 and
110).
Areas Under the Curve for any Normal Distribution
99.7%
95.4%
68.3%
H – 30
M– 20
M – lo
μ+ Ισ
μ+ 3σ
M + 20
Sketch a normal curve for the probability density function. Label the horizontal axis with values of 50, 60, 70, 80, 90, 100, and 110.
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Transcribed Image Text:A random variable is normally distributed with a mean of u = 80 and a standard deviation of o = 10. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 50 and 110). Areas Under the Curve for any Normal Distribution 99.7% 95.4% 68.3% H – 30 M– 20 M – lo μ+ Ισ μ+ 3σ M + 20 Sketch a normal curve for the probability density function. Label the horizontal axis with values of 50, 60, 70, 80, 90, 100, and 110. 110 100 90 80 70 60 50 50 60 70 80 90 100 110 60 80 100 110 90 70 50
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