A random variable is normally distributed with a mean of

=60

and a standard deviation of

=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 at30and90).

Areas Under the Curve for any Normal Distribution

• 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: (3), (2), (1),, (+ 1), (+ 2) and (+ 3).
• The curve enters the viewing window just above the axis at (3), reaches a peak at, and exits the viewing window just above the axis at (+ 3).
• Three percent values are given.
• 68.3% of the shaded area lies between (1) and (+ 1)
• 95.4% of the shaded area lies between (2) and (+ 2)
• 99.7% of the shaded area lies between (3) and (+ 3)

Sketch a normal curve for the probability density function. Label the horizontal axis with values of30,40,50,60,70,80, and90.

• 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 seven evenly-spaced ticklabels on the horizontal axis; listed from left to right, in the order in which they appear on the horizontal axis, they are: 90, 80, 70, 60, 50, 40, 30.
• The maximum point of the curve is over ticklabel: 60.

• 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 seven evenly-spaced ticklabels on the horizontal axis; listed from left to right, in the order in which they appear on the horizontal axis, they are: 30, 40, 50, 60, 70, 80, 90.
• The maximum point of the curve is over ticklabel: 60.

• 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 seven evenly-spaced ticklabels on the horizontal axis; listed from left to right, in the order in which they appear on the horizontal axis, they are: 40, 60, 80, 90, 70, 50, 30.
• The maximum point of the curve is over ticklabel: 90.

• 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 seven evenly-spaced ticklabels on the horizontal axis; listed from left to right, in the order in which they appear on the horizontal axis, they are: 30, 50, 70, 90, 80, 60, 40.
• The maximum point of the curve is over ticklabel: 90.

(b)What is the probability the random variable will assume a value between50and70? (Round your answer to three decimal places.)

(c)What is the probability the random variable will assume a value between30and90? (Round your answer to three decimal places.)