Respuesta :
Answer:
0.0996 or 0.1
Step-by-step explanation:
First, find the phat. x/n
Then find the z-score: p^ - 0.45 divided by the square root of 0.45(1-0.45)/750.
Hope this helps!
Using the normal approximation to the binomial distribution, it is found that there is a 0.093 = 9.3% probability that fewer than 320 out of the 750 adults over 65 in the study suffer from one or more of the conditions under consideration.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].
In this problem:
- Sample of 750 adults, hence [tex]n = 750[/tex].
- 45% of the adults suffer from one or more of the conditions, hence [tex]p = 0.45[/tex].
For the approximation, the mean and the standard deviation are given by:
[tex]\mu = np = 750(0.45) = 337.5[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{750(0.45)(0.55)} = 13.6244[/tex]
Using continuity correction, the probability that fewer than 320 out of the 750 adults over 65 in the study suffer from one or more of the conditions under consideration is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the p-value of Z when X = 319.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{319.5 - 337.5}{13.6244}[/tex]
[tex]Z = -1.32[/tex]
[tex]Z = -1.32[/tex] has a p-value of 0.093.
0.093 = 9.3% probability that fewer than 320 out of the 750 adults over 65 in the study suffer from one or more of the conditions under consideration.
A similar problem is given at https://brainly.com/question/24261244
