The probability that more than 30 Americans of the 50 in the survey approve of the missile strikes is .3859
<h3>How to determine if the normal distribution can be applied?</h3>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
<h3>The mean of the sampling proportion? </h3>This is the same as the population proportion.
So, the mean of the sampling proportion is 0.58
<h3>The standard deviation sampling proportion? </h3>This is calculated using:
So, we have:
σ = 0.0698
<h3>That no more than 25 Americans approve of the missile strikes? </h3>Start by calculating the p-value
p = 25/50
p = 0.5
The z-score is:
This gives
This gives
z = -1.15
Using the z-table of probability, the requested probability is:
P(z ≤ -1.15) = 0.1251
<h3>The probability that more than 30 approved of the missile strikes? </h3>Start by calculating the p-value
p = 30/50
p = 0.6
The z-score is:
This gives
This gives
z = 0.29
Using the z-table of probability, the requested probability is:
P(z > 0.29) = 0.3859
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