CB.Stats.VAR-5.F: Describe the effects of linear transformations of parameters of random variables.

Describe the effects of linear transformations of parameters of random variables.

Example Problems

Lila shoots 5 free throws during her basketball warmup. The arc height of each shot has a mean of

\mu = 11\text{ feet}

and a standard deviation of

\sigma = 0.4\text{ feet}

. We can assume that the arc heights of her shots are independent from each other. Let

T

be the total of the arc heights of her 5 shots.

Find the mean of

T

,

\mu_T

.

Priya is a high school volleyball player. During a match, she hits 4 serves. The speeds of her serves have a mean of

\mu = 42

miles per hour and a standard deviation of

\sigma = 3

miles per hour. We can assume that the speeds of her serves are independent from each other. Let

T

be the total of the speeds of her 4 serves.

Find the mean of

T

,

\mu_T

.

At a bakery, a chef adds 6 scoops of flour to each batch of bread dough. The scoops of flour have a mean mass of

\mu = 125\text{ grams}

and a standard deviation of

\sigma = 4\text{ grams}

. We can assume that the masses of the scoops are independent of each other. Let

T

be the total mass of flour in a randomly chosen batch.

Find the mean of

T

,

\mu_T

.

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