Question

A survey asks 1200 workers, "has the economy forced you to reduce the amount of vacation you plan to take this year?" Thirty-five percent of those survey selected. The random variable represents the number of workers who are reducing the amount of vacation. Find the mean, variance and standard deviation of the binomial deviation of the binomial distribution.

Answer 1

If a variable is binomially distributed with n trials and a success probability of p, then the mean = np, variance = np(1–p) and standard deviation = square root of variance.

In this case, n = 1200, p = 0.35. So, mean = (1200)(0.35) = 420,
variance = (1200)(0.35)(1–0.35) = 273,
standard deviation = square root of variance = √273 = 16.52.

Answer 2

Mean = 420

Variance = 273

Standard Deviation = 17

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

Let us tackle the problem.

A survey asks 1200 workers → n = 1200

Thirty-five percent of those survey selected → p = 35% = 0.35

To find the mean of a binomial distribution, we can use the following formula:

$Mean = n \times p$

$Mean = 1200 \times 0.35$

$\boxed {Mean = 420}$

To find the variance of a binomial distribution, we can use the following formula:

$Variance = n \times p \times (1 - p)$

$Variance = 1200 \times 0.35 \times (1 - 0.35)$

$Variance = 1200 \times 0.35 \times 0.65$

$\boxed {Variance = 273}$

To find the standard deviation of a binomial distribution, we can use the following formula:

$Standard ~ Deviation = \sqrt{Variance}$

$Standard ~ Deviation = \sqrt{273}$

$\boxed {Standard ~ Deviation \approx 17}$

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation