In a Young"s two-slit experinemt a pieve of glass with an index of refraction $n$ and a thickness $L$ is placed in front of the upper slit. (a) Describe qualitatively what happens to the interference pattern. (b) Derive an expression for the intensity $I$ of the light at points on a screen as a function of $n, L$, and $\theta$. Here $\theta$ is the usual angle measured from the center of the two slits. That is, determine the equation analogous to Eq. (35.14) but that also involves $L$ and $n$ for the glass plate. (c) From your result in part (b) derive an expression for the values of $\theta$ that locate the maxima in the interference pattern [that is, derive an equation analogous to Eq.

Supermodels are sometimes criticized on the grounds that their low weights encourage unhealthy eating habits among young women. Use the following weights (in pounds) of randomly selected supermodels.

125 (Taylor) 119 (Auermann) 128 (Schiffer) 125 (Bundchen) 119 (Turlington) 127 (Hall) 105 (Moss) 123 (Mazza) 110 (Reilly) 103 (Barton)

Find the sample size necessary to estimate the mean weight of all supermodels so that there is 95% confidence that the sample mean is in error by no more than 2 lb. Assume that a pilot study suggests that the weights of all supermodels have a standard deviation of 7.5 lb.

Choose the best way to rewrite each underlined word or word group.

When you listen to music, do you think about $\frac{{ its }}{(1)}$ origins? People typically respond to this question by saying, $\frac{{My friends and me }}{(2)}$ don't think about this. $\frac{{ We }}{(3)}$ just like the music." Music has been an important part of $\frac{{ours }}{(4)}$ existence since the beginning of humankind. Historians tell $\frac{{scholars and we }}{(5)}$ that humans began to sing as soon as $\frac{{them }}{(6)}$ developed language. Like us, people in ancient civilizations used $\frac{{they're }}{(7)}$ voices to express feelings. However, most ancient music was not meant to entertain. Ancient musicians played $\frac{{them}}{(8)}$mainly during important ceremonies. The ancient people $\frac{{whom}}{(9)}$ were most interested in music were the early Greeks. They thought music had a positive role in the education of young people. They also believed that young people $\frac{{ who listened to good music }}{(10)}$ would become better adults.

A. My friends and us

B. My friends and I

C. Me and my friends

D. Correct as is

When the number of trials, $n$, is large, binomial probability tables may not be available. Furthermore, if a computer is not available, hand calculations will be tedious. As an alternative, the Poisson distribution can be used to approximate the binomial distribution when $n$ is large and $p$ is small. Here the mean of the Poisson distribution is taken to be $\mu=n p$. That is, when $n$ is large and $p$ is small, we can use the Poisson formula with $\mu=n p$ to calculate binomial probabilities, and we will obtain results close to those we would obtain by using the binomial formula. A common rule is to use this approximation when $n / p \geq 500$.

To illustrate this approximation, in the movie Coma, a young female intern at a Boston hospital was very upset when her friend, a young nurse, went into a coma during routine anesthesia at the hospital. Upon investigation, she found that $10$ of the last $30,000$ healthy patients at the hospital had gone into comas during routine anesthesias. When she confronted the hospital administrator with this fact and the fact that the national average was $6$ out of $100,000$ healthy patients going into comas during routine anesthesias, the administrator replied that $10$ out of $30,000$ was still quite small and thus not that unusual.

Use the Poisson distribution to approximate the probability that $10$ or more of $30,000$ healthy patients would slip into comas during routine anesthesias, if in fact the true average at the hospital was $6$ in $100,000$ . Hint: $\mu=n p=$ $30,000(6 / 100,000)=1.8$

Solve each problem. Winona paid $\$ 100$ for a lifetime membership to Friends of the Zoo, so that she could gain admittance to the zoo for only $\$ 1$ per visit. Write Winona's average cost per visit $C$ as a function of the number of visits when she has visited $x$ times. What is her average cost per visit when she has visited the zoo $100$ times? Graph the function for $x>0$. What happens to her average cost per visit if she starts when she is young and visits the zoo every day?

Do birds learn to time their breeding? Blue titmice eat caterpillars. The birds would like lots of caterpillars around when they have young to feed, but they must breed much earlier. Do the birds learn from one year’s experience when to time their breeding next year? Researchers randomly assigned 7 pairs of birds to have the natural caterpillar supply supplemented while feeding their young and another 6 pairs to serve as a control group relying on natural food supply. The next year, they measured how many days after the caterpillar peak the birds produced their nestlings. Rather than comparing the two groups in each year, we could compare the behavior of each group in the first and second years. The study report says: “Our main prediction was that females receiving additional food in the nestling period should not change laying date the next year, whereas controls, which (in our area) breed too late in their first year, were expected to advance their laying date in the second year.” Comparing days behind the caterpillar peak in Years 1 and 2 gave t=0.63 for the control group and t=-2.63 for the supplemented group. Explain why these t-values do not agree with the prediction.

Choose the best way to rewrite each underlined word or word group.

When you listen to music, do you think about $\frac{{ its }}{(1)}$ origins? People typically respond to this question by saying, $\frac{{My friends and me }}{(2)}$ don't think about this. $\frac{{ We }}{(3)}$ just like the music." Music has been an important part of $\frac{{ours }}{(4)}$ existence since the beginning of humankind. Historians tell $\frac{{scholars and we }}{(5)}$ that humans began to sing as soon as $\frac{{them }}{(6)}$ developed language. Like us, people in ancient civilizations used $\frac{{they're }}{(7)}$ voices to express feelings. However, most ancient music was not meant to entertain. Ancient musicians played $\frac{{them}}{(8)}$mainly during important ceremonies. The ancient people $\frac{{whom}}{(9)}$ were most interested in music were the early Greeks. They thought music had a positive role in the education of young people. They also believed that young people $\frac{{ who listened to good music }}{(10)}$ would become better adults.

A. Us

B. Them

C. You

D. Correct as is

Choose a young person (aged 19 to 25) at random and ask, "In the past seven days, how many days did you watch television?" Call the response X for short. Here is the probability distribution for X:

$$\begin{array}{lcccccccc} \hline \text { Days } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \text { Probability } & 0.04 & 0.03 & 0.06 & 0.08 & 0.09 & 0.08 & 0.05 & ? ? ? \\ \hline \end{array}$$

The mean of the random variable X is $\mu_{X}=5.44$ and the standard deviation is $\sigma_{\mathrm{X}}=2.14.$ Interpret these values.

In each of the following sentences, draw a line through the error in comparison. Then, above it, write the correct form. If the error is a missing word, draw a caret ($_\wedge$) where the word should be inserted and then write the word above the caret.

Examples

1. Of the two of you, she is clearly $\overset{\textit{\color{#c34632}{taller}}}{\sout{\text{tallest}}}$.

2. Rhode Island is smaller than $\overset{\textit{\color{#c34632}{other}}}{{\text{any state\ last}}}$.

Miguel is the most sincerest young man I’ve ever met.

Aeropostale, Inc. is a specialty fashion retailer targeting young adults. The income before income tax expense and interest expense for four recent years follow (in millions):

$$\begin{array}{lrrrr} & \text { Year 4 } & \text { Year 3 } & \text { Year 2 } & \text { Year 1 } \\ \hline \text { Income (loss) before income tax expense } & \$(132.1) & \$(135.6) & \$ 91.7 & \$ 129.1 \\ \text { Interest expense } & 8.8 & 0.9 & 0.5 & 0.4 \end{array}$$

Compute the time interest earned ratio for each year. (Round to one decimal place.)

Fill each blank with the most appropriate word from the vocabulary list below.

VOCABULARY LIST

$$\begin{array}{lll}\text { juxtaposition } & \text { puberty } & \text { primeval } \\ \text { obsolescent } & \text { abstemious } & \text { dross } \\ \text { squalid } & \text { puerile } & \text { obsolete } \\ \text { senility } & \text { immaculate } & \text { nonage } \\ \text { longevity } & \text { jetsam } & \text { carrion }\end{array}$$

During his legal minority, the young monarch had heeded his _______ advisers, but, once past his he took absolute personal control.

In an experiment on the behavior of young children, each subject is placed in an area with five toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows:

$$\begin{array}{lcccccc} \hline \text { Number of toys } x_{i} & 0 & 1 & 2 & 3 & 4 & 5 \\ \text { Probability } \rho_{i} & 0.03 & 0.16 & 0.30 & 0.23 & 0.17 & ? ? \\ \hline \end{array}$$

Write the event "child plays with 5 toys" in terms of X. Then find its probability.

In the following sentence, a verb does not agree with its subject, or a pronoun does not agree with its antecedent. Cross out any incorrect verb or pronoun. Then, above it, write the correct form. If the sentence is already correct, write C next to its number.

Examples:

Most were satisfied with $\overset{\textit{\color{#c34632}{their}}}{\sout{\text{his or her}}}$ grade.

A squirrel or a bird $\overset{\textit{\color{#c34632}{has}}}{\sout{\text{have}}}$ been eating the blackberries off the vine.

Most of the games at the fair are intended for very young children.

Which statement accurately compares the themes presented in both selections? A. "Neutral Tones" offers a lighthearted message about love, while Adam Bede suggests that love is a somber experience. B. Both selections use nature imagery to convey a message about the fragile beauty of young love. C. "Neutral Tones" contemplates a romantic breakup, while Adam Bede describes the hopeful beginning of a romance. D. "Neutral Tones" implies that love grows over time, while Adam Bede implies that love fades over time.