Remember back in Chapter 5 when we used the equation

$$SAT = 40 \times ACT + 150$$

to convert an ACT score into a SAT score. Let's use this transformation again, now with random variables. Suppose your school has a mean ACT score of 29. What would its equivalent mean SAT score be?

Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as 1600, while the maximum ACT composite score is 36. Since the two exams use very different scales, comparisons of performance are difficult. A convenient rule of thumb is

$$S A T = 40 \times A C T + 150;$$

that is, multiply an ACT score by 40 and add 150 points to estimate the equivalent SAT score. An admissions officer reported the following statistics about the ACT scores of 2355 students who applied to her college one year. Find the summaries of equivalent SAT scores.

$$\left. \begin{array} { l } { \text { Lowest score } = 19 \quad \text {Mean} = 27\quad \text {Standard deviation} = 3 } \\ { Q 3 = 30 } \quad { \text { Median } = 28 \quad \text {IQR} = 6 } \end{array} \right.$$

A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them. a) How many broken eggs do you expect to get? b) What 's the standard deviation? c) What assumptions did you have to make about the eggs in order to answer this question? Do you think that assumption is warranted? Explain.

An employer pays a mean salary for a 5-day workweek of $1250 with a standard deviation of$129. On the weekends, his salary expenses have a mean of $450 with a standard deviation of$57. What is the mean and standard deviation of his total weekly salaries?

A line has parametric equations

$$x = 2 + t \quad y = 3 t \quad z = 5 - t$$

and a plane has equation 5x - 2y - 2z = 1. (a) For what value of t does the corresponding point on the line intersect the plane? (b) At what point do the line and the plane intersect?

Write the number in standard notation.

$$5.23 \times 10 ^ { 0 }$$

A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will actually grow is 18, with a standard deviation of 1.2 seeds. You buy 5 different seed packets. a) How many bad seeds do you expect to get? b) What’s the standard deviation? c) What assumptions did you make about the seeds? Do you think that assumption is warranted? Explain.

Solve:

$$x ^ { 6 } + 17 x ^ { 3 } + 16 = 0$$

Write each product using the Distributive Property. Then simplify. 11(28)

A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them. How many broken eggs do you expect to get?

In which of the following groupings do each of the three ions have the same number of electrons? How many electrons do they have? (a)

$$O^{2-}, F^-, N^{3-}$$

(b)

$$Na^+, K^+, Li^+$$

(c)

$$K^+, P^{3-}, Ar$$

(d)

$$F^-, Cl^-, Br^-$$

A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them. a) How many broken eggs do you expect to get? b) What’s the standard deviation? c) What assumptions did you have to make about the eggs in order to answer this question?

Find the percent change. Round to the nearest percent. $168.45 to$234.56

A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them. What's the standard deviation?