/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 55. Watch the salt! A study investig... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q 55. (page 140)

Watch the salt! A study investigated about 3000 meals ordered from

Chipotle restaurants use the online site Grubhub. Researchers calculated the sodium content (in milligrams) for each order based on Chipotle鈥檚 published nutrition information. The distribution of sodium content is approximately Normal with a mean of 2000mg and a standard deviation of 500mg.10About what percent of the meals ordered exceeded the recommended daily allowance of 2400 mg of sodium?

Short Answer

Expert verified

Around 21.19 percent of the meals ordered included more sodium than the daily limit of 2400 mg.

Step by step solution

01

Given information

Daily allowance,x=2400mg

Mean,渭=2000mg

Standard deviation,蟽=500mg

02

Concept

The formula used:z=x鈭�渭蟽

03

Calculation

Calculate the Z鈭�score,

z=x鈭�渭蟽=2400mg鈭�2000mg500mg=0.80

To find the equivalent probability, use the normal probability table in the appendix.

See the usual normal probability table for P(z<0.80)in the row that starts with 0.8and the column that starts with.00.

P(x>2400)=P(z<0.80)=1鈭�P(z>0.80)=1鈭�0.7881=0.2119=21.19%

Therefore,

Around 21.19 percent of the meals ordered included more sodium than the daily limit of 2400 mg.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Household incomes Refer to Exercise 10Here are summary statistics for the state median household incomes:

nMeanSDMinQ1MedQ3Max
5051742.448210.643664146071500095702071836

a. Find and interpret the z-score for North Carolina, with a median household income of $41,553

b. New Jersey had a standardized score of 1.82Find New Jersey鈥檚 median household income for that year.

The density of the earth In 1798, the English scientist Henry Cavendish measured the density of the earth several times by careful work with a torsion balance. The variable recorded was the density of the earth as a multiple of the density of water. A Normal probability plot of the data is shown.16 Use the graph to determine if this distribution of density measurement is approximately Normal.

At some fast-food restaurants, customers who want a lid for their drinks get them from a large stack near the straws, napkins, and condiments. The lids are made with a small amount of flexibility so they can be stretched across the mouth of the cup and then snugly secured. When lids are too small or too large, customers can get very frustrated, especially if they end up spilling their drinks. At one particular restaurant, large drink cups require lids with a 鈥渄iameter鈥� of between 3.95 and 4.05 inches. The restaurant鈥檚 lid supplier claims that the diameter of its large lids follows a Normal distribution with a mean of 3.98 inches and a standard deviation of 0.02 inches. Assume that the supplier鈥檚 claim is true.

Put a lid on it!

a. What percent of large lids are too small to fit?

b. What percent of large lids are too big to fit?

c. Compare your answers to parts (a) and (b). Does it make sense for the lid manufacturer to try to make one of these values larger than the other? Why or why not?

Carbon dioxide emissions The following figure is a Normal probability plot of the emissions of carbon dioxide CO2 per person in 48 countries.15 Use the graph to determine if this distribution of CO2 emissions is approximately Normal.

Measuring bone density Individuals with low bone density (osteoporosis) have a high risk of broken bones (fractures). Physicians who are concerned about low bone density in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). The bone density results for a patient who undergoes a DEXA test usually are reported in grams per square centimeter (g/cm2) and in standardized units. Judy, who is 25years old, has her bone density measured using DEXA. Her results indicate bone density in the hip of 948 g/cm2 and a standardized score of z=鈭�1.45The mean bone density in the hip is 956 g/cm2in the reference population of 25-year-old women like Judy.

a. Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score reveals about her bone density.

b. Use the information provided to calculate the standard deviation of bone density in the reference population.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.