The chance of getting a sample proportion of 80% or greater is 0.0062.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We are given that a poll shows that 60% of students enjoy mathematics.
A random sample of 25 students showed that 80% of them enjoy mathematics.
Let = sample proportion of students who play sports
The z-score probability distribution for the sample proportion is given by;
Z = [tex]\dfrac{p'-p}{\sqrt{\dfrac{p'(1-p')}{n}}}[/tex] ~ N(0,1)
where,
p' = sample proportion of students who enjoy mathematics. = 80%
p = population proportion of students who enjoy mathematics = 60%
n = sample of students = 20
Now, the chance of getting a sample proportion of 80% or greater is given by = P( p'≥ 80%)
P( p' ≥ 80%) = P( [tex]\dfrac{0.8-0.6}{\sqrt{\dfrac{0.8(1-0.6)}{25}}}[/tex] )
P(Z ≥ 2.5) = 1 - P(Z < 2.5)
P(Z ≥ 2.5) = 1 - 0.9938 = 0.0062
The above probability is calculated by looking at the value of x = 2.5 in the z-table which has an area of 0.9938
Hence, the chance of getting a sample proportion of 80% or greater is 0.0062.
Therefore the chance of getting a sample proportion of 80% or greater is 0.0062.
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