A population is normally distributed with

=200

and

=10.

a.

Find the probability that a value randomly selected from this population will have a value greater than

215.

b.

Find the probability that a value randomly selected from this population will have a value less than

185.

c.

Find the probability that a value randomly selected from this population will have a value between

185

and

215.

a.P(x>215)=

b.P(x<185)=

c. P(185

An expensive watch is powered by a 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 year and is normally distributed.a. Determine the probability that the watch's battery will last longer than 3.8 years.b. Calculate the probability that thewatch's battery will last more than 2.15 years.c. Compute thelength-of-life value for which 15% of the watch's batteries last longer.

a. The probability that the battery will last longer than 3.8 years is

b. The probability that the battery will last more than 2.15 years is

c. The length-of-life value for which 15% of the batteries last longer is years.

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to two per 15

minutes. Complete parts a and b below.Click here to view page 1 of the table of Poisson probabilities.

a. Determine the probability that in a given 15-minutesegment, no customers will arrive at the ATM.The probability is

b. What is the probability that fewer than five customers will arrive in a 45-minute segment?The probability is