Let *x* represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the *x* distribution is about $15 and the estimated standard deviation is about $8.

Consider a random sample of *n* = 100 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

A) What is the probability that x is between $13 and $17? (Round your answer to four decimal places.

B) Let us assume that *x* has a distribution that is approximately normal. What is the probability that *x* is between $13 and $17? (Round your answer to four decimal places.

### Want to see the full answer?

Check out a sample Q&A here*arrow_forward*Check out a sample Q&A here

*star_border*

## Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned)…

A: a) The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the…

Q: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned)…

A: Given data Mean μ = 10 Standard deviation ? = 9 a) Sample size n = 40

Q: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned)…

A: Click to see the answer

Q: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: In the probability distribution to the right, the random variable X represents the number of…

A: Solution 0 0.269 0 0 0 1 0.571 0.571 1 0.571 2 0.123 0.246 4 0.492 3 0.031 0.093 9…

Q: Let x be the number of potential weapons detected by a metal detector at an airport on a given day.…

A: Given : x P(x) 0 0.14 1 0.28 2 0.22 3 0.21 4 0.15

Q: Suppose that the probability distribution for the number of errors, X, on pages from business…

A: Given, X P (X) 0 0.81 1 0.17 2 0.02 To find, Find the mean number of errors per…

Q: Consider the following probability distribution where random variable X denotes the number of cups…

A: Given data is x 0 1 2 3 4 5 P(x) 0.35 0.40 0.16 0.02 0.02

Q: Suppose the probability distribution of x, the number of defective tires on a randomly selected car…

A: The random variable x be the number of defective tires on a randomly selected car checked at a…

*question_answer*

Q: Suppose that the random variable xx, shown below, represents the number times . P(x) represents the…

A: Click to see the answer

*question_answer*

Q: Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned)…

A: Solution:

*question_answer*

Q: Suppose that the random variable z, shown below, represents the number times . P(x) represents the…

A: Given data is x P(x) 0 0.3028 1 0.2745 2 0.2629 3 0.0889 4 0.0406 5 0.0303 6+…

*question_answer*

Q: The average age of residents in a large residential retirement community is 69 years with standard…

A: Let, X: The age of residents in a large residential retirement community. X : The sample mean age.…

*question_answer*

Q: Suppose that, on average, electricians earn approximately u $54,000 per year in the United States.…

A: GivenMean(μ)=54000standard deviation(σ)=12000sample size(n)=4

*question_answer*

Q: Suppose the probability distribution of x, the number of defective tires on a randomly selected car…

A: Click to see the answer

*question_answer*

Q: Using these data as his probability distribution for the number of cases, the legal staff…

A: Let X be the random variable denoting the number of cases. Consider the following table, X…

*question_answer*

Q: The following table lists the probability distribution for cash prizes in a lottery conducted at…

A: Given, X 0 10 100 500 P(X) 0.45 0.30 0.20 0.05 Mean = E(X)= summation(X*p(x)) Variance=…

*question_answer*

Q: Suppose that the random variable xx, shown below, represents the number of speeding tickets a person…

A: Solution x P(x) 0 0.2775 1 0.2546 2 0.2388 3 0.1736 4 0.0449 5 0.0106 6+ 0.0000…

*question_answer*

Q: Suppose that the random variable xx, shown below, represents the number of speeding tickets a person…

A: (a) Obtain the probability that a randomly selected person has received four tickets in a…

*question_answer*

Q: Suppose that the random variable r, shown below, represents the number times. P(x) represents the…

A: Let , the random variable X be the number of speeding tickets. The probability distribution table…

*question_answer*

Q: The number of telephone calls arriving at an exchange during any given minute between noon and 1:00…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

*question_answer*

Q: Suppose you randomly select 10 women from a population of women, and 15 men from a population of men…

A: Given below randomly selected 10 women from a population of women, and 15 men from a population of…

*question_answer*

Q: Suppose that the random variable xx, shown below, represents the number of speeding tickets a person…

A: Given, Number of spending tickets a person received in three years periods and below the probability…

*question_answer*

Q: Suppose you randomly select 10 women from a population of women, and 15 men from a population of men…

A: From the given information, Women weight is denoted by n1=10 and Men weight is denoted by n2=15…

*question_answer*

A: Solution: From the given information, the probability distribution of X is

*question_answer*

Q: Suppose that the random variable xx, shown below, represents the number times . P(x)P(x) represents…

A: Part A The probability that a randomly selected person has received four tickets in a three-year…

*question_answer*

Q: For a group of four 70-year old men, the probability distribution for the number z who live through…

A: Given :

*question_answer*

Q: Determine whether the following is a probability distribution. If not, identify the requirement that…

A: Conditions for the discrete probability distribution: 1. The sum of all probability is equal to 1.…

*question_answer*

Q: A Wendy’s manager performed a study to determine a probability distribution for the number of…

A: The table shows the probability distribution for the number of people.

*question_answer*

Q: The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a…

A: given data is X P(X) 0 0.95 20 0.049 100 0.001 we have to find standard deviation of the…

*question_answer*

Q: he table shows the probability distribution of the number of days (x) to complete a construction…

A: Given that Probability distribution data X 1 2 3 4 5 6 P(x) 0.104 - 0.312 0.240 0.098 0.017…

*question_answer*

Q: The following table lists the probability distribution of a discrete random variable x: x| 2 3 4 5 6…

A: The probability distribution of X is given. In order to find the standard deviation we need to find…

*question_answer*

Q: Below is the relative-frequency table of the probability distribution for the discrete random…

A: Solution: Let X be the number of cars owned by families in New York. From the given information, the…

*question_answer*

Q: The following table lists the probability distribution of a discrete random variable x: x 2 3 5 6 4…

A: Given problem Given that The following table lists the probability distribution of a discrete…

*question_answer*

A: As per the guidelines we are allowed to solve maximum of 3 subparts Please repost the question if…

*question_answer*

Q: A market research team compiled the following discrete probability distribution for families…

A: discrete probability dist

*question_answer*

Q: Consider the discrete probability distribution, 10 12 18 20 P(x) 0.2 0.1 0.1 i. Calculate P(x > 18)…

A: Click to see the answer

*question_answer*

Q: Suppose that the random variable x, shown below, represents the number times . P(x) represents the…

A: a) The random variable x defines the number of times a randomly selected person having received that…

*question_answer*

Q: Find the mean and variance of the uniform probability distribution given by f(x)= 1/n for x = 1, 2,…

A: The given uniform probability distribution is, f(x)= 1n for x = 1, 2, 3,....., n The mean of…

*question_answer*

Q: Consider the following discrete probability distribution. 15 0.20 22 34 P(X - x) 40 0.16 0.38 0.26…

A: (a) We total probability = 1 ∑P(x) = 0.2 + 0.38 + 0.26 + 0.16 = 1 Therefore the total…

*question_answer*

Q: The average age of residents in a large residential retirement community is 69 years with standard…

A: From the provided information, Mean (µ) = 69 years Standard deviation (σ) = 5.8 years X~N (69, 5.8)…

*question_answer*

Q: Consider selecting a household at random in the rural area of a country. Define the random variable…

A: We have given that the probability distribution of X in tabulation form. The random variable is the…

*question_answer*

A: Solution: From the given information, the probability distribution of X is

*question_answer*

Q: Let X be a random variable with probability distribution as follows: 3 f (x) | 1 1 1 3 Find the…

A: Click to see the answer

*question_answer*

Q: Illustrate a probability distribution of a random variable X showing the number of face mask sold…

A: Given, Day Number of Face Mask 1 25 2 20 3 15 4 14 5 15 6 10 7 12 8 10 9 15…

*question_answer*

Q: Suppose the waiting time (in minutes) for cars in fuel station, X, is normally distributed with mean…

A: The random variable X follows normal distribution. The population mean is 10. The population…

*question_answer*

Q: Consider the following discrete probability distribution. 5 10 15 20 P(X = x) 0.12 0.41 0.30 0.17…

A: Click to see the answer

*question_answer*

Q: Let X represent the full length of a certain species of newt. Assume that X has a normal probability…

A: It is given that, X~N(110.8, 6.22) A sample size n=220 is to be taken. So, by the CLT, you can…

*question_answer*

Q: Assume that 12 jurors are randomly selected from a population in which 86% of the people are…

A: The probability of exactly 7 Mexican Americans among 12 jurors is obtained below: P(x=7)=0.0148.

*question_answer*

Q: have during the first 7 years of their marriage. F follows the following probability distribution…

A: Here calculate in table for F.P(F) AND F2 P(F) IN FURTHER STEP FOR MEAN AND STANDARD DEVIATION