Questions: 78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below. Find the mean of the binomial distribution. μ=4.7 (Round to the nearest tenth as needed.) Find the variance of the binomial distribution. σ^2=1.0 (Round to the nearest tenth as needed.) Find the standard deviation of the binomial distribution. σ= (Round to the nearest tenth as needed.)

78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below. Find the mean of the binomial distribution. μ=4.7 (Round to the nearest tenth as needed.) Find the variance of the binomial distribution. σ^2=1.0 (Round to the nearest tenth as needed.) Find the standard deviation of the binomial distribution. σ= (Round to the nearest tenth as needed.)
Transcript text: $78 \%$ of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below. Find the mean of the binomial distribution. $\mu=4.7$ (Round to the nearest tenth as needed.) Find the variance of the binomial distribution. $\sigma^{2}=1.0$ (Round to the nearest tenth as needed.) Find the standard deviation of the binomial distribution. $\sigma=$ $\square$ (Round to the nearest tenth as needed.)
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Mean

The mean \( \mu \) of a binomial distribution can be calculated using the formula:

\[ \mu = n \cdot p \]

Where:

  • \( n = 6 \) (the number of trials)
  • \( p = 0.78 \) (the probability of success)

Substituting the values:

\[ \mu = 6 \cdot 0.78 = 4.68 \approx 4.7 \]

Step 2: Calculate the Variance

The variance \( \sigma^2 \) of a binomial distribution is given by the formula:

\[ \sigma^2 = n \cdot p \cdot q \]

Where:

  • \( q = 1 - p = 0.22 \) (the probability of failure)

Substituting the values:

\[ \sigma^2 = 6 \cdot 0.78 \cdot 0.22 = 1.0336 \approx 1.0 \]

Step 3: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{n \cdot p \cdot q} \]

Substituting the values:

\[ \sigma = \sqrt{6 \cdot 0.78 \cdot 0.22} = \sqrt{1.0336} \approx 1.0 \]

Final Answer

  • Mean \( \mu \approx 4.7 \)
  • Variance \( \sigma^2 \approx 1.0 \)
  • Standard Deviation \( \sigma \approx 1.0 \)

Thus, the final answers are:

\[ \boxed{\mu = 4.7} \] \[ \boxed{\sigma^2 = 1.0} \] \[ \boxed{\sigma = 1.0} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
You own investment A and 10 bonds of bond B. The total value of your holdings is 14,633.4. Investment A is expected to make annual payments forever. The first payment for investment A is expected to be 227 and all subsequent payments are expected to increase by 2.19 percent per year forever. The expected return for investment A is 11.47 percent per year and the first payment will be made in 1 year. Bond B has a coupon rate of 19.30 percent, par value of 1000, YTM of X percent, 17 years until maturity, and semiannual coupons with the next coupon expected in 6 months. What is X ? Input instructions: Input your answer as the number that appears before the percentage sign. For example, enter 9.86 for %, 86 % (do not enter .0986 or 9.86 %). Round your answer to at least 2 decimal places.
failedAnswered
¿Qué hora es la clase de español?
failedAnswered
The following table shows Ellie's utility from consuming slices of pie and cans of Dr. Pepper. Slices of Pie Marginal Utility from Last Slice Cans of Dr. Pepper Marginal Utility from Last Can --- --- --- --- 0 - 0 - 1 120 1 120 2 100 2 60 3 80 3 45 4 60 4 30 5 40 5 20 6 20 6 15 Suppose Ellie has 6 per week to spend on pie and Dr. Pepper and that the price of a slice of pie is 1.00. 1.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of 2.00. Label this point 'A': 2.) Use the point drawing tool to plot Ellie's demand for Dr. Pepper at a price of 0.50. Label this point 'B'. 3.) Use the line drawing tool to connect the dots to form Ellie's demand curve. Properly label this line. Carefully follow the instructions above, and only draw the required objects.
failedAnswered
APPLYING THE AREA FORMULA 1. Use the formula to calculate the areas of the following triangles: triangle ABC, triangle EFG, triangle JKL and triangle MNP.
failedAnswered
D1 receptor increase in CAMP D2 receptor decrease in CAMP beta 1 receptor increase in CAMP alpha 2 receptor decrease in CAMP beta 2 receptor increase in CAMP m2 receptor decrease in CAMP 5 HT1 receptor decrease in CAMP 5 HT4 receptor increase in CAMP