/*! 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. 6.6 The weight of tomatoes chosen at... [FREE SOLUTION] | 91影视

91影视

The weight of tomatoes chosen at random from a bin at the farmer's market follows a Normal distribution with mean =10ounces and standard deviation =1ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

a. Normal, with mean 10 ounces and standard deviation 1 ounce.

b. Normal, with mean 40 ounces and standard deviation 2 ounces.

c. Normal, with mean 40 ounces and standard deviation 4 ounces.

d. binomial, with mean 40 ounces and standard deviation 2 ounces.

e. binomial, with mean 40 ounces and standard deviation 4 ounces.

Short Answer

Expert verified

(b) T is a random variable with a mean of 40 ounces and a standard deviation of 2 ounces.

Step by step solution

01

Given Information

The weight of tomatoes randomly selected from a bin at the farmer's market follows a normal distribution with a mean of ten and a standard deviation of one dollar.

Consider the random variable t, which is specified as the weight of tomatoes.

Therefore,

t~N10,12
02

Explanation for correct option

According to the information provided,

t~N10,12

As a result of the normal distribution property,

nt~Nn(10),nI2

As a result, the T random variable (4 tomatoes weight) will be used.

T4t~N4(10),412T~N40,22

Thus, the correct option is "b".

03

Explanation for incorrect option

Option (a) Normal, with mean 10 ounces and standard deviation 1 ounce is not the correct answer.

Option (c) Normal, with mean 40 ounces and standard deviation 4 ouncesis not the correct answer.

Option (d) binomial, with mean 40 ounces and standard deviation 2 ounces is not the correct answer.

Option (e) binomial, with mean 40 ounces and standard deviation 4 ounces is not the correct answer.

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

Exercises 21 and 22 examine how Benford鈥檚 law (Exercise 9) can be used to detect fraud.

Benford鈥檚 law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1 to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a) What鈥檚 P(Y<6)? According to Benford鈥檚 law (see Exercise 9), what proportion of first digits in the employee鈥檚 expense amounts should be greater than 6? How could this information be used to detect a fake expense report?

(b) Explain why the mean of the random variable Yis located at the solid red line in the figure.

(c) According to Benford鈥檚 law, the expected value of the first digit is X=3.441. Explain how this information could be used to detect a fake expense report.

Spoofing (4.2) To collect information such as passwords, online criminals use "spoofing" to direct Internet users to fraudulent websites. In one study of Internet fraud, students were warned about spoofing and then asked to log into their university account starting from the university's home page. In some cases, the log-in link led to the genuine dialog box. In others, the box looked genuine but, in fact, was linked to a different site that recorded the ID and password the student entered. The box that appeared for each student was determined at random. An alert student could detect the fraud by looking at the true Internet address displayed in the browser status bar, but most just entered their ID and password.

a. Is this an observational study or an experiment? Justify your answer.

b. What are the explanatory and response variables? Identify each variable as categorical or quantitative.

The time X it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with mean 15 minutes and standard deviation 6.5 minutes. Once he parks his car in his reserved space, it takes 5 more minutes for him to walk to his office. Let T= the total time it takes Hattan to reach his office on a randomly selected day, so T=X+5. Describe the shape, center, and variability of the probability distribution of T.

Kids and toys 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:

Part (a). Write the event 鈥渃hild plays with 5 toys鈥 in terms of X. Then find its probability.

Part (b). What鈥檚 the probability that a randomly selected subject plays with at most 3 toys?

Roulette Marti decides to keep placing a 1$ bet on number 15 in consecutive spins of a roulette wheel until she wins. On any spin, there's a 1-in-38 chance that the ball will land in the 15 slot.

a. How many spins do you expect it to take for Marti to win?

b. Would you be surprised if Marti won in 3 or fewer spins? Compute an appropriate probability to support your answer.

See all solutions

Recommended explanations on Math Textbooks

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.