Problem 17BSC

Too Young to Tat Based on a Harris poll of 370 adults who regret getting tattoos, 20% say that they were too young when they got their tattoos.

a. For randomly selected groups of 370 adults who regret getting tattoos, find the mean and standard deviation for the number who say that they were too young when they got their tattoos.

b. For a randomly selected group of 370 adults who regret getting tattoos, would 90 be an unusually low or high number who say that they were too young when they got their tattoos?

Problem 17BSC

Answer:

Step1 of 2:

We have Based on a Harris poll of 370 adults who regret getting tattoos, 20% say that they were too young when they got their tattoos.

That is n = 370 and p =20% = 0.20

The mean and standard deviation for the number who say that they were too young when they got their tattoos is given by

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 370 and p = 0.20.

q = 1 - p

= 1 - 0.20.

= 0.8

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

With mean E(x) = np and variance var(x) = npq

Consider,

E(x) = np

= 3700.20

= 74

Therefore,E(x) = 74

var(x) = npq

= 3700.200.80

= 59.2

Standard deviation is given by =

=

= 7.6941.

8.

Step2 of 2:

b).

For a randomly selected group of 370 adults who regret getting tattoos,

Consider,A range rule It is especially important to interpret results. The range rule of thumb suggests that values are unusual if they lie outside of these limits:

Minimum = and Maximum =

1).Minimum =

= 74 - 2(8)

= 58.

2).Maximum =

= 74 + 2(8)

= 90.

Therefore, 90 lies between intervals that is (58, 90) hence unusually effective.