Researchers published a study in which they considered the incidence among the elderly of various mental health conditions such as dementia, bi-polar disorder, obsessive compulsive disorder, delirium, and Alzheimer's disease. In the U. S., 45% of adults over 65 suffer from one or more of the conditions considered in the study. Calculate the probability that fewer than 320 out of the n = 750 adults over 65 in the study suffer from one or more of the conditions under consideration. Give your answer accurate to three decimal places in decimal form. (Example: 0.398)

P (z) = 0.005

Step-by-step explanation:

From problem statement:

We know:

Researchers study 45 % adults over 65 suffering disorders

Sample 320 out of 750

then p = 320 / 750 = 0,4267

1. - Test hypothesis

H₀ null hypothesis ⇒ p₀ = 0,45

Hₐ alternative hypothesis ⇒ p₀ < 0.45

We calculate the z (s) as:

z (s) = (p - p₀) / √ p₀*q₀/n ⇒ z (s) = (0.4267 - 0.45) / √ (0.45*0,55) / 750 z (s) = - 0.0233 * √750 / 0.2475

z (s) = - 0.6381/0.2475 ⇒ z (s) = - 2.57

We look for - 2.57 in z tabl to find the probability of fewer than 320 out of 750 suffer of disorder, and find

P (z) = 0.0051

P (z) = 0.005