3 Consider an investment whose return is normally distribute

3. Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%.

a. Determine the probability of losing money.

b. If we increase the standard deviation to 10%, the probability of suffering a loss becomes:

c. What is the meaning of the standard deviation?

4. Lifetime of Alkaline battery (measured in hours) is exponentially distributed with (MU exponent) = 0.05 .

a. What is the mean and standard deviation of the battery\'s lifetime?

b. Find the probability that a battery will last between 10 and 15 hours?

c. What is the probability that a battery will last for more than 20 hours?

5. A checkout counter at a supermarket completes the process according to an exponential distribution with a service rate of 6 per hour. A customer arrives at the checkout counter. Find the probability of the following events:

a. The service is completed in less than 5 minutes.

b. The customer leaves the checkout counter more than 10 minutes after arriving.

c. The service is completed in a time between 5 and 8 minutes

Solution

Please post the three questions separetely. Only Question 3 will be answered here. Answer part is in bold.

3. Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%. Here, X follows N(10,5²).

a. Determine the probability of losing money.

P(Losing Money) = P(X<0) = 0.0228 (Obtained in R with pnorm(0,mean=10,sd=5)).

b. If we increase the standard deviation to 10%, the probability of suffering a loss becomes:

In this case, X follows N(10,10²). Hence,

P(Losing Money) = P(X<0) =  0.1587. (Obtained in R with pnorm(0,mean=10,sd=10)).

c. What is the meaning of the standard deviation?

Standard deviation is a measure of spread/dispersion and indicated how much the spread of the variable is. The coverage percentage of the RV depends on the assumed probability distribution.