Respuesta :
Answer:
0.0222 is the probability that in a city of 10,000 people there are more than 120 people who are bipolar.
Step-by-step explanation:
We are given the following in the question:
Probability of adult suffering from bipolar disorder =
[tex]p =\dfrac{1}{100} = 0.01[/tex]
Sample size, n = 10000
We have to use normal approximation to the binomial distribution to estimate the probability.
Normal approximation:
[tex]\mu = np = 10000(0.01) = 10\\\sigma = \sqrt{np(1-p)} = \sqrt{10000(0.01)(1-0.01)} = 9.95[/tex]
The distribution of adults suffering from bipolar disorder follows a normal distribution with mean 100 and standard deviation 9.5
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to evaluate:
P(more than 120 people are bipolar)
P(x > 120)
[tex]P( x > 120) = P( z > \displaystyle\frac{120 - 100}{9.95}) = P(z > 2.010)[/tex]
[tex]= 1 - P(z \leq 2.010)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 610) = 1 - 0.9778 = 0.0222 = 2.22\%[/tex]
0.0222 is the probability that in a city of 10,000 people there are more than 120 people who are bipolar.
