Question

About 6% of the population has a particular genetic mutation. A group of 600 people is randomly selected.Find the mean (x) and standard deviation (o) for the number of people with the genetic mutation in suchgroups of size 600. Round your answers to 3 places after the decimal point, if necessary.

Answer 1

From the question, we were told that about 6% of the general population has a genetic mutation.

So, if we take a random sample of 600 people, about 6% of those 600 people will have that mutation.

(a) Find the mean.

To find the mean, recall:

Percentage = 6% = 0.06

Group size = 600

Mean (x) = Group size * percentage

Mean (x) = 600 * 0.06

Mean (x) = 36

(b) Standard deviation (o)

To find the Standard deviation, we use the formular:

`\begin{gathered} S\text{ = }√(n)\left(p\right)\left(1-p\right)\text{ } \\ Where\text{ n is the sample size, p is the probability.} \\ So, \\ S\text{ = }√(600)\text{ \lparen0.06\rparen\lparen1-0.06\rparen} \\ S\text{ = }√(600)\text{ \lparen0.06\rparen\lparen0.94\rparen} \\ S\text{ = 24.4949 \lparen0.06\rparen\lparen0.94\rparen} \\ S\text{ = 1.3815} \\ S\text{ = 1.382 \lparen rounded to 3 decimal places\rparen} \end{gathered}`