91影视

Ms. Hall gave her class a 10-question multiple-choice quiz.

Let $X=$the number of questions that a randomly selected student in the class answered correctly. The computer output gives information about the probability distribution of $X$. To determine each student鈥檚 grade on the quiz (out of $100$), Ms. Hall will multiply his or her number of correct answers by $5$and then add $50.$Let $G=$the grade of a randomly chosen student in the class.

Easy quiz

a. Find the median of $G$.

b. Find the interquartile range (IQR) of $G$.

Ms. Hall gave her class a 10-question multiple-choice quiz.

Let$X=$the number of questions that a randomly selected student in the class answered correctly. The computer output gives information about the probability distribution of $X$. To determine each student鈥檚 grade on the quiz (out of $100$), Ms. Hall will multiply his or her number of correct answers by $5$and then add $50$. Let $G=$the grade of a randomly chosen student in the class.

More easy quiz

a. Find the mean of $G$.

b. Find the range of $G$.

During the winter months, the temperatures at the Starneses鈥� Colorado cabin can stay well below freezing $(32掳For0掳C)$for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at $50掳F.$She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years鈥� worth of data, the temperature $T$in the cabin at midnight on a randomly selected night can be modeled by a Normal distribution with mean $8.5掳C$and standard deviation $2.25掳C$. Let $Y=$the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that$F=(9/5)C+32)$.

a. Find the mean of $Y$.

b. Calculate and interpret the standard deviation of $Y.$

c. Find the probability that the midnight temperature in the cabin is less than $40掳F$.

A company鈥檚 single-serving cereal boxes advertise $1.63$ounces of cereal. In fact, the amount of cereal X in a randomly selected box can be modeled by a Normal distribution with a mean of $1.70$ounces and a standard deviation of $0.03$ounce. Let $Y=$the excess amount of cereal beyond what鈥檚 advertised in a randomly selected box, measured in grams ($1\mathrm{ounce}=28.35\mathrm{grams}$).

a. Find the mean of $Y$.

b. Calculate and interpret the standard deviation of $Y.$

c. Find the probability of getting at least $1gram$more cereal than advertised.

El Dorado Community College has a main campus in the suburbs and a downtown campus. The amount X spent on tuition by a randomly selected student at the main campus has mean 732.50 and standard deviation 103. The amount Y spent on tuition by a randomly selected student at the downtown campus has mean 825 and standard deviation 126.50. Suppose we randomly select one full-time student from each of the two campuses. Calculate and interpret the mean of the sum$\mathrm{S}=\mathrm{X}+\mathrm{Y}.$

Get on the boat! Refer to Exercise 3. Make a histogram of the probability distribution. Describe its shape.

Typographical and spelling errors can be either 鈥渘onword errors鈥� or 鈥渨ord errors.鈥� A nonword error is not a real word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� A word error is a real word, but not the right word, as when 鈥渓ose鈥� is typed as 鈥渓oose.鈥� When students are asked to write a 250-word essay (without spell-checking), the number of nonword errors X in a randomly selected essay has mean 2.1 and standard deviation 1.136. The number of word errors Y in the essay has mean 1.0 and standard deviation 1.0. Calculate and interpret the mean of the sum S = X + Y.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures academic motivation and study habits. The SSHA score F of a randomly selected female student at a large university has mean 120 and standard deviation 28, and the SSHA score M of a randomly selected male student at the university has mean 105 and standard deviation 35. Suppose we select one male student and one female student at random from this university and give them the SSHA test. Calculate and interpret the mean of the difference $\mathrm{D}=\mathrm{F}鈭�\mathrm{M}$in their scores.

Sul茅鈥檚 job is just a few bus stops away from his house. While it can be faster to take the bus to work than to walk, the travel time is more variable due to traffic. The commute time B if Sul茅 takes the bus to work on a randomly selected day has mean 12 minutes and standard deviation 4 minutes. The commute time W if Sul茅 walks to work on a randomly selected day has mean 16 minutes and standard deviation 1 minute. Calculate and interpret the mean of the difference $\mathrm{D}=\mathrm{B}鈭�\mathrm{W}$ in the time it would take Sul茅 to get to work on a randomly selected day?

At the main campus, full-time students pay \(50 per unit. At the downtown campus, full-time students pay \)55 per unit. Find the mean of the difference D (Main 鈭� Downtown) in the number of units that the two randomly selected students take.