Question

2. + 0.33/1 points Previous Answers ASWESBE9 6.E.009. My Notes + Ask Your Teacher A random variable is normally distributed with a mean of u = 90 and a standard deviation of g = 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 60 and 120). Areas Under the Curve for any Normal Distribution 99.7% 95.4% * 68.3% • A graph with 1 bell-shaped, continuous, and symmetric curve above the horizontal axis is given. The area under the curve is shaded. • There are 7 equally spaced labels on the axis; from left to right they are: (L - 30), (U - 2 0), (LL – 1 0), , ( + 1 0), (L2 + 2 O) and (u + 3 0). • The curve enters the viewing window just above the axis at (u - 30), reaches a peak at , and exits the viewing window just above the axis at (+ 30). • Three percent values are given. • 68.3% of the shaded area lies between (LL - 10) and (LL + 10 . 95.4% of the shaded area lies between (- 20) and (4 + 20) . 99.7% of the shaded area lies between (1 - 30) and (u + 3 0) Sketch a normal curve for the probability density function. Label the horizontal axis with values of 60, 70, 80, 90, 100, 110, and 120.

Answer 1

b)

as 80 and 100 are 1 standard deviation from the mean, therefore probability =0.683

c) for 70 and 110 are 2 standard deviation from the mean, therefore probability = 0.954