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:
[tex]Mean = n \times p[/tex]
[tex]Mean = 1200 \times 0.35[/tex]
[tex]\boxed {Mean = 420}[/tex]
To find the variance of a binomial distribution, we can use the following formula:
[tex]Variance = n \times p \times (1 - p)[/tex]
[tex]Variance = 1200 \times 0.35 \times (1 - 0.35)[/tex]
[tex]Variance = 1200 \times 0.35 \times 0.65[/tex]
[tex]\boxed {Variance = 273}[/tex]
To find the standard deviation of a binomial distribution, we can use the following formula:
[tex]Standard ~ Deviation = \sqrt{Variance}[/tex]
[tex]Standard ~ Deviation = \sqrt{273}[/tex]
[tex]\boxed {Standard ~ Deviation \approx 17}[/tex]
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
