Answer:
The Required Probability is 0.8525
Step-by-step explanation:
Given:
Number of people, n = 134
Proportion of people voted , p = 22% = 0.22
To find: the Probability that fewer than 32 of 134 eligible voters voted.
First we find the mean and Standard deviation,
Means,
[tex]\mu=n\times p=134\times0.22=29.48[/tex]
Standard Deviation,
[tex]\sigma=\sqrt{n\times p\times q}=\sqrt{134\times0.22\times0.78}=\sqrt{22.9944}=4.795[/tex]
Now the Probability,
[tex]P(X<32)=P(X\leq34.5)=P(\frac{X-\mu}{\sigma}\leq\frac{34.5-29.48}{4.795})=P(z\leq1.047)=0.8525\::(using\,z-score\:table)[/tex]
Therefore, The Required Probability is 0.8525
The distribution of apple follows a normal distribution.
The probability that fewer than 32 of 134 eligible voters voted is 0.70
The given parameters are:
[tex]p =22\%[/tex] --- proportion of those that voted
[tex]n = 134[/tex] --- standard deviation
[tex]x = 32[/tex]
First, we calculate the mean
[tex]\mu = np[/tex]
So, we have:
[tex]\mu = 134 \times 22\%[/tex]
[tex]\mu = 29.48[/tex]
Next, calculate the standard deviation
[tex]\sigma = \sqrt{\mu \times (1 - p)}[/tex]
So, we have:
[tex]\sigma = \sqrt{29.48 \times (1 - 22\%)}[/tex]
[tex]\sigma = 4.80[/tex]
Next, we calculate the z score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Substitute known values
[tex]z = \frac{32 - 29.48}{4.80}[/tex]
[tex]z = \frac{2.52}{4.80}[/tex]
[tex]z = 0.525[/tex]
So, the probability that fewer than 32 voted is:
[tex]P(X<x) = P(Z<z)[/tex]
This gives
[tex]P(X<32) = P(Z<0.525)[/tex]
From z-score table, we have:
[tex]P(z>0.525) = 0.70021[/tex]
This means that:
[tex]P(x<32) =0.70021[/tex]
Approximate
[tex]P(x<32) =0.70[/tex]
Hence, the probability that fewer than 32 of 134 eligible voters voted is 0.70
Read more about probabilities of normal distributions at:
https://brainly.com/question/6476990
