Answer:
(a) Probability that fewer than 100 will be under 18 years of age is 0.19655.
(b) Probability that 200 or more will be over 59 years of age is 0.00449.
Step-by-step explanation:
We are given that over 70% of households play such games. Of those individuals who play video and computer games, 18% are under 18 years old, 53% are 18-59 years old, and 29% are over 59 years old.
(a) A sample of 600 people is selected and we have to find the probability that fewer than 100 will be under 18 years of age.
The z score probability distribution for sample proportion is given by;
Z =
~ N(0,1)
where,
= sample proportion of people =
= 16.67%
p = population proportion of people under 18 years old = 18%
n = sample of people = 600
Now, probability that fewer than 100 will be under 18 years of age is given by = P(
< 0.167)
P(
< 0.167) = P(
<
) = P(Z < -0.854) = 1 - P(Z
0.854)
= 1 - 0.80345 = <u>0.19655</u>
<em>The above probability is calculated by looking at the value of x = 0.854 in the z table which will lie between x = 0.85 and x = 0.86.</em>
(b) A sample of 800 people is selected and we have to find the probability that 200 or more will be over 59 years of age.
The z score probability distribution for sample proportion is given by;
Z =
~ N(0,1)
where,
= sample proportion of people =
= 25%
p = population proportion of people over 59 years old = 29%
n = sample of people = 800
Now, probability that 200 or more will be over 59 years of age is given by = P(
0.25)
P(
0.25) = P(
) = P(Z
-2.613) = P(Z
2.613)
= 1 - 0.99551 = <u>0.00449</u>
<em>The above probability is calculated by looking at the value of x = 2.613 in the z table which will lie between x = 2.61 and x = 2.62.</em>