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Sagot :
The probability that more than 30 Americans of the 50 in the survey approve of the missile strikes is .3859
How to determine if the normal distribution can be applied?
The given parameters are:
Sample size, n = 50
Population proportion, p = 0.58
By central limit theorem (CLT), the normal approximation can be used with this distribution because the sample size is greater than 30
The mean of the sampling proportion?
This is the same as the population proportion.
So, the mean of the sampling proportion is 0.58
The standard deviation sampling proportion?
This is calculated using:
[tex]\sigma = \sqrt{\frac{p(1 - p)}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{0.58 * (1 - 0.58)}{50}}[/tex]
σ = 0.0698
That no more than 25 Americans approve of the missile strikes?
Start by calculating the p-value
p = 25/50
p = 0.5
The z-score is:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{0.5 - 0.58}{0.0698}[/tex]
This gives
z = -1.15
Using the z-table of probability, the requested probability is:
P(z ≤ -1.15) = 0.1251
The probability that more than 30 approved of the missile strikes?
Start by calculating the p-value
p = 30/50
p = 0.6
The z-score is:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{0.6 - 0.58}{0.0698}[/tex]
This gives
z = 0.29
Using the z-table of probability, the requested probability is:
P(z > 0.29) = 0.3859
Read more about normal distribution at:
https://brainly.com/question/4079902
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