Conceptual Overview: Explore how standard deviation measures the risk of an investment.

For both U$.$S$.$ Water $($blue curve$)$ and Martin Products $($red curve$)$ the expected return is $10\%.$ However, the spread of possible outcomes for U$.$S$.$ Water is "tighter" $($i$.$e$.,$ closer to the expected return of $10\%)$ than the spread for Martin Products. The depicted distributions are both normal distributions, but with different standard deviations. Use the slider at the bottom to change the standard deviation for the distribution of outcomes for Martin Products. Drag the vertical dashed line on the graph to the left or right to observe the probability of exceeding a particular rate of return.

As the standard deviation for Martin Products' distribution increases, the distribution for Martin Products:

becomes steeper and more like the distribution for U$.$S$.$ Water

does not change

becomes flatter and less like the distribution for U$.$S$.$ Water

might either become steeper or flatter

$2.$ Use the slider to set the standard deviation for Martin Products to be $6\mathrm{.}0.$ The probability of having a rate of return of at least $5\%($move the cursor to $5\mathrm{.}0)$

is greater for U$.$S$.$ Water than for Martin Products

is the same for both U$.$S$.$ Water and the Martin Products distribution

is greater for Martin Products than U$.$S$.$ Water

cannot be determined

$3.$ Use the slider to set the standard deviation for the Martin Products distribution to $8\mathrm{.}0.$ The probability of having a rate of return of at least $10\%($move the vertical line to $10\mathrm{.}0)$

is greater for U$.$S$.$ Water than for Martin Products

is the same for both U$.$S$.$ Water and the Martin Products distribution

is greater for Martin Products than U$.$S$.$ Water

cannot be determined

$4.$ Suppose the standard deviation for the Martin Products Distribution is $4\mathrm{.}0.$ If an investor is hoping for a return of at least $13\%,$ the chances that investing in Martin Products will return at least $13\%$

are much less than in investing in U$.$S$.$ Water

are the same as investing in U$.$S$.$ Water

are greater than in investing in U$.$S$.$ Water

cannot be determined

$5.$ As the standard deviation of outcomes for Martin Products increases, investing in Martin Products becomes riskier because

the range of outcomes having some probability becomes wider

an outcome at or near the expected return of $10\%$ becomes less likely

although the chances of some big gains increase, the chances for some big losses also increase.

all of the above reasons

none of the above reasons