$11$ Jane is a financial advisor. She informs a client that the expected return on a portfolio is $=7\mathrm{.}5$ percent, with a standard deviation of $\backslash$sigma $=10$ percent.

What is the probability that the return would be above $15$ percent?

a $0\mathrm{.}2699$

b $0\mathrm{.}2546$

c $0\mathrm{.}2402$

d $0\mathrm{.}2266$

$12$ Jennifer is a financial consultant.

She tells her client that the probability of making a return on a portfolio above $15$ percent is $9\%.$

The standard deviation of the return is $\backslash$sigma $=5.$

What is the mean $($expected$)$ return on the portfolio?

a $9\mathrm{.}13$

b $8\mathrm{.}30$

c $7\mathrm{.}54$

d $6\mathrm{.}86$

$13$ Bob is an investment manager. He tells his client that the probability of making a positive return is $0\mathrm{.}90.$

Returns are normally distributed with a mean of $\backslash$mu $=8\mathrm{.}5$ percent.

What is the risk, measured by standard deviation, that Bob assumes in his calculations?

a $6\mathrm{.}63$

b $7\mathrm{.}37$

c $8\mathrm{.}19$

d $9\mathrm{.}10$

$14$ A filling machine for soda bottles can be set for any mean value but it cannot be set to have every bottle contain exactly the same amount of soda.

Assume that the distribution of ounces per bottle is normal with a standard deviation of $\backslash$sigma $=0\mathrm{.}25$ ounces.

At what mean level should the filling machine be so that the probability that a bottle contains less than $24$ ounces is $0\mathrm{.}019.$

a $25\mathrm{.}64$

b $25\mathrm{.}26$

c $24\mathrm{.}89$

d $24\mathrm{.}52$

Boston, Massachusetts, averages $213$ sunny days per year.

Assume that the number of sunny days follows a normal distribution with a standard deviation of $19$ days.

$15$ What is the probability that Boston has less than $200$ sunny days in a given year?

a $0\mathrm{.}2671$

b $0\mathrm{.}2568$

c $0\mathrm{.}2469$

d $0\mathrm{.}2374$

$16$ Los Angeles averages $268$ sunny days per year.

What is probability that Boston has at least as many sunny days as Los Angeles?

a $0\mathrm{.}0019$

b $0\mathrm{.}0032$

c $0\mathrm{.}0053$

d $0\mathrm{.}0088$

$17$ Suppose a dismal year in Boston is one when the number of sunny days is in the bottom $10\%$ for that year.

At most, how many sunny days must occur annually for it to be a dismal year in Boston?

a $186\mathrm{.}8$

b $188\mathrm{.}7$

c $190\mathrm{.}6$

d $192\mathrm{.}5$

$18$ A university restricts its admission to students whose SAT scores are in the top $7\%$ of all scores.

David is wondering if he can be admitted.

David has a combined verbal and math SAT score of $1165.$

The distribution of SAT scores is normal with a mean of $1070$ and a standard deviation of $62.$

is David's score high enough to be admitted?

a The minimum score for admission is $1138$ David will not be admitted.

b The minimum score for admission is $1150$ David will not be admitted.

c The minimum score for admission is $1161$ David will be admitted.

d The minimum score for admission is $1173$ David will be admitted.

$19$ In the previous question, $95\%$ of test scores are within $\backslash$pm $\_\_\_\_\_\_$ from the mean test score.

a $120\mathrm{.}3$

b $121\mathrm{.}5$

c $122\mathrm{.}7$

d $124\mathrm{.}0$