Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 74 students in the high school and found a mean savings of 4500 dollars with a standard deviation of 1300 dollars. At the 95% confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest whole number. (Do not write +- ). Answer:

A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 7474 students in the high school and found a mean savings of 45004500 dollars with a standard deviation of 13001300 dollars. At the 95% 95 \% confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest whole number. (Do not write ± \pm ).\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Use normal distributions to approximate binomial distributionsright chevron icon

Full solution

Q. A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 7474 students in the high school and found a mean savings of 45004500 dollars with a standard deviation of 13001300 dollars. At the 95% 95 \% confidence level, use the normal distribution/empirical rule to estimate the margin of error for the mean, rounding to the nearest whole number. (Do not write ± \pm ).\newlineAnswer:
  1. Identify Given Values: Identify the given values from the problem.\newlineWe are given:\newline- Mean savings (xˉ\bar{x}) = \(4500\)\(\newline\)- Standard deviation (\(s\)) = 13001300\newline- Sample size (nn) = 7474\newline- Confidence level = 9595%
  2. Determine Confidence Level: Determine the z-score that corresponds to the 95%95\% confidence level.\newlineFor a 95%95\% confidence level, the z-score that corresponds to the confidence interval is approximately 1.961.96. This is because 95%95\% of the data falls within 1.961.96 standard deviations from the mean in a normal distribution.
  3. Calculate Margin of Error: Calculate the margin of error using the formula for the margin of error at a given confidence level.\newlineThe margin of error (E) is calculated using the formula:\newlineE=z×sn E = z \times \frac{s}{\sqrt{n}} \newlinewhere z z is the z-score, s s is the standard deviation, and n n is the sample size.
  4. Calculate Margin of Error: Plug in the values and calculate the margin of error.\newlineE=1.96×130074 E = 1.96 \times \frac{1300}{\sqrt{74}} \newlineE=1.96×13008.6023 E = 1.96 \times \frac{1300}{8.6023} (rounded to four decimal places for the square root of 7474)\newlineE=1.96×151.1365 E = 1.96 \times 151.1365 (rounded to four decimal places for the division)\newlineE=296.2275 E = 296.2275
  5. Round Margin of Error: Round the margin of error to the nearest whole number.\newlineThe margin of error rounded to the nearest whole number is 296296.

More problems from Use normal distributions to approximate binomial distributions

Question
A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well. \newlineIf the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?\newlineWrite your answer as a decimal rounded to the nearest thousandth.
Get tutor helpright-arrow

Posted 7 months ago

Question
There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____
Get tutor helpright-arrow

Posted 9 months ago

Question
There are two different raffles you can enter.\newlineIn raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are 1,0001,000 in the raffle, each costing `$11`.\newlineRaffle B is for a `$370` prize. Out of 125125 tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline[A]Raffle A\text{[A]Raffle A}\newline[B]Raffle B\text{[B]Raffle B}
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 4949 and standard deviation 2525.\newlineWhat is the probability that XX is between 2424 and 7474??\newlineUse the 0.68−0.95−0.9970.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.\newline____
Get tutor helpright-arrow

Posted 9 months ago

Question
XX is a normally distributed random variable with mean 6565 and standard deviation 88.\newlineWhat is the probability that XX is between 6262 and 6868??\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____
Get tutor helpright-arrow

Posted 9 months ago

Question
Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 33, the bottom 30%30\% of the values are those less than ______.
Get tutor helpright-arrow

Posted 9 months ago

Question
Y Y is the number of desserts available in a randomly chosen restaurant.\newlineIs the random variable Y Y discrete or continuous?\newlineChoices:\newline[A]discrete \text{[A]discrete} \newline[B]continuous \text{[B]continuous}
Get tutor helpright-arrow

Posted 9 months ago

Question
Which of the following functions are continuous for all real numbers?\newlineg(x)=ln⁡(x) g(x)=\ln (x) \newlinef(x)=1x f(x)=\frac{1}{x} \newlineChoose 11 answer:\newline(A) g g only\newline(B) f f only\newline(C) Both g g and f f \newlineD Neither g g nor f f
Get tutor helpright-arrow

Posted 9 months ago

Question
Which of the following functions are continuous at x=−1 x=-1 ?\newlineg(x)=sin⁡(x+1) g(x)=\sin (x+1) \newlinef(x)=1x−1 f(x)=\frac{1}{x-1} \newlineChoose 11 answer:\newline(A) g g only\newline(B) f f only\newline(C) Both g g and f f \newline(D) Neither g g nor f f
Get tutor helpright-arrow

Posted 8 months ago

Question
Let g g be a continuous function on the closed interval [−1,4] [-1,4] , where g(−1)=−4 g(-1)=-4 and g(4)=1 g(4)=1 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) g(c)=−3 g(c)=-3 for at least one c c between −1-1 and 44\newline(B) g(c)=3 g(c)=3 for at least one c c between −4-4 and 11\newline(C) g(c)=−3 g(c)=-3 for at least one c c between −4-4 and 11\newline(D) g(c)=3 g(c)=3 for at least one c c between −1-1 and 44
Get tutor helpright-arrow

Posted 8 months ago

View all (18)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant