Sketch a normal curve for the probability density function. Label the horizontal axis with values of 75, 80, 85, 90, 95, 100, and 105. 105 100 95 90 85 80 75 75 85 95 105 100 90 80 75 80 85 90 95 100 105 80 90 100 105 95 85 75 (b) What is the probability the random variable will assume a value between 80 and 100? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 85 and 95? (Round your answer to three decimal places.)

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A random variable is normally distributed with a mean of u = 90 and a standard deviation of o = 5.
(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 75 and 105).
Areas Under the Curve for any Normal Distribution
99.7%
95.4%
+ 68.3% -
H-30
H-lo
μ+ Ισ
++30
H-20
H + 20
Transcribed Image Text:A random variable is normally distributed with a mean of u = 90 and a standard deviation of o = 5. (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 75 and 105). Areas Under the Curve for any Normal Distribution 99.7% 95.4% + 68.3% - H-30 H-lo μ+ Ισ ++30 H-20 H + 20
Sketch a normal curve for the probability density function. Label the horizontal axis with values of 75, 80, 85, 90, 95, 100, and 105.
105
100
95
90
85
80
75
75
105
85
95
100
90
80
75
80
85
90
95
100
105
80
90
100
105
95
85
75
(b) What is the probability the random variable will assume a value between 80 and 100? (Round your answer to three decimal places.)
(c) What is the probability the random variable will assume a value between 85 and 95? (Round your answer to three decimal places.)
Transcribed Image Text:Sketch a normal curve for the probability density function. Label the horizontal axis with values of 75, 80, 85, 90, 95, 100, and 105. 105 100 95 90 85 80 75 75 105 85 95 100 90 80 75 80 85 90 95 100 105 80 90 100 105 95 85 75 (b) What is the probability the random variable will assume a value between 80 and 100? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 85 and 95? (Round your answer to three decimal places.)
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