Modeling Data Distributions

The distribution of annual profit at a chain of stores was approximately normal with mean \mu = \$66{,}000μ=$66,000mu, equals, dollar sign, 66, comma, 000 and standard deviation \sigma = \$21{,}000σ=$21,000sigma, equals, dollar sign, 21, comma, 000.

$48,000

What proportion of exam scores are between 82 and 85.68

.2379

What is the maximum resting pulse rate for students who are eligible to join the weight-lifting club?

77 bpm

What is the minimum waist circumference of men whom the store aims to serve?

99 cm

A town hosted two races—a full marathon and a half marathon—and recorded the finishing times for both races. Here are some summary statistics:

Rex and Lisa finished with equally fast times relative to their races

Here are some summary statistics for the durations for which candles from a certain company burn.

The berry-scented pillar candle

Consider the density curve below.Which of the following statements are true?

The mean of the density curve is less than the median. The area underneath the density curve is 1.

The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives 20.520, point, 5 years; the standard deviation is 3.93, point, 9 years.

.15%

A set of shirt prices are normally distributed with a mean of 45 dollars and a standard deviation of 5 dollars. What proportion of shirt prices are between 37 dollars and 59.35 point, 35 dollars?

0.9431

The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 101010 years was approximately normal with mean \mu = 85μ=85mu, equals, 85 days and standard deviation \sigma = 29σ=29sigma, equals, 29 days. The property management company intends to update the kitchen appliances in the apartments that were empty for top 10\%10%10, percent of durations.

123

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.512the standard deviation is 2.42 years. Use the empirical rule (68-95-99.7)to estimate the probability of a lion living between 5.35 and 10.11

15.85%

The distribution of average wait times in drive-through restaurant lines in one town was approximately normal with mean \mu = 185μ=185mu, equals, 185 seconds and standard deviation \sigma = 11σ=11sigma, equals, 11 seconds.

170 seconds

The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 101010 years was approximately normal with mean 85 days and standard deviation 29 days. The property management company tags the files of the apartments that were empty for the shortest 5\%5%5, percent of durations to have priority cleaning the next time their residents move out. What is the maximum duration for which an apartment remained empty for the company to tag its file?

37%

Matheus ordered hydrangeas (a kind of flower) to decorate for a wedding. The stem plot gives the diameters, in inches, of the 353535 heads of the hydrangeas that arrived.

37th Percentile

Use the empirical rule (68-95-99.7\%)( estimate the probability of a lizard living between 2.52 and 4.34

81.5%

Isabella is a 202020-year-old undergraduate student and Hannah is a 333333-year-old graduate student at the university.

Isabella and Hannah are equally young relative to their groups.

The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives 22.422, point, 4 years; the standard deviation is 2.72.72, point, 7 years.

2.35

Before applying to law school in the US, students need to take an exam called the LSAT. Before applying to medical school, students need to take an exam called the MCAT. Here are some summary statistics for each exam:

Juwan scored better on the LSAT relative to others who took that test.

Vitor (who is male) and Manuela (who is female) both completed 808080 sit-ups on the fitness test.

Manuela

The Senate minority leader that year was 66 years old, while the House of Representatives minority leader was 76 years old.

The House of Representatives minority leader

A set of average city temperatures in August are normally distributed with a mean of 21.25 ^\circ \text{C}21.25∘C21, point, 25, degrees, start text, C, end text and a standard deviation of 2 ^\circ \text{C}2∘C2, degrees, start text, C, end text.

.1024

A set of average city temperatures in October are normally distributed with a mean of 20.6 ^\and a standard deviation of 2 ^

.4032

A set of college student heights are normally distributed with a mean of 170.4170.4170, point, 4 centimeters and a standard deviation of 101010 centimeters.

.5184

A set of computer science exam scores are normally distributed with a mean of 71.3371.3371, point, 33 points and a standard deviation of 333 points.

.8533

A set of average city temperatures in September are normally distributed with a mean of 21.02and a standard deviation of 2

.9539

What proportion of electric toothbrush prices are between 104.60104.60104, point, 60 dollars and 108.20108.20108, point, 20 dollars?

0.0099

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 161616 years; the standard deviation is 1.71.71, point, 7 years.

16%

The lifespans of seals in a particular zoo are normally distributed. The average seal lives 13.813.813, point, 8 years; the standard deviation is 3.23.23, point, 2 years.

2.5%

The distribution of reading scale scores in the 4^\text{th}4th4, start superscript, start text, t, h, end text, end superscript grade at Truman Elementary School was approximately normal with mean \mu = 221μ=221mu, equals, 221 and standard deviation \sigma = 36σ=36sigma, equals, 36. Educational researchers are conducting an intervention experiment. To participate in the experiment, a student must have a reading scale score in the lower 50\%50%50, percent of the scores in their grade level.

221

The distribution of reading scale scores in the 4^\text{th}4th4, start superscript, start text, t, h, end text, end superscript grade at Roosevelt Elementary School was approximately normal with mean \mu = 221μ=221mu, equals, 221 and standard deviation \sigma = 36σ=36sigma, equals, 36.

252

The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives 3.13.13, point, 1 years; the standard deviation is 0.60.60, point, 6 years.

84%

The distribution of resting pulse rates of all students at Santa Maria high school was approximately normal with mean \mu = 80μ=80mu, equals, 80 beats per minute and standard deviation \sigma = 9σ=9sigma, equals, 9 beats per minute. The school nurse plans to provide additional screening to students whose resting pulse rates are in the top 30\%30%30, percent of the students who were tested.

85 bpm

The employee e-mail accounts in one company are using a mean of 1.071.071, point, 07 gigabytes of memory with a standard deviation of 0.210.210, point, 21 gigabytes.

Mean: 10961Standard deviation: 215

What will be the mean and standard deviation of the distribution of excess cleaning solution, in milliliters?

Mean: 30mL Deviation: 45 mL

school sells pizza slices at the concession stand during each sporting event. The school sells a mean of 200200200 slices per event with a standard deviation of 252525 slices.

mean: $240 sd: $50

Suppose the jar actually holds 105105105 candies, and we want to convert each guess to its error—that is, we'll subtract 105105105 from each guess to see how far above or how far below the guess was from the correct number.

mean: -20 sd: 12

In one county, the farms had a mean harvested area of 103103103 acres with a standard deviation of 999 acres. What will be the mean and standard deviation of the distribution of area in square kilometers?

mean: .412 standard deviation: .036

In Mr. Britt's class the distribution of ages of his students has a mean of 115115115 months and a standard deviation of 3.63.63, point, 6 months.

mean: 119 months sd: 3.6 months

Yuki weighed several soil samples, each filling a quarter liter measuring cup. The distribution of masses has a mean of 215\,\text{g}215g215, start text, g, end text and a standard deviation of 60\,\text{g}60g60, start text, g, end text. After recording her measurements, Yuki realized that she had forgotten to subtract the mass of the measuring cup, which is 20\,\text{g}20g20, start text, g, end text.

mean: 195 sd:60

A group of Americans participated in a study that involved taking their temperatures during exercise in extreme heat. The participants had a mean body temperature of 104 and a standard deviation of 2

mean: 40 sd: 1.11