A random variable is normally distributed with a mean of

=40

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 at10and70).

(a)What is the probability the random variable will assume a value between 10 and 70? (Round your answer to three decimal places.)

(b)What is the probability the random variable will assume a value between 30 and 50? (Round your answer to three decimal places.)