Answer:
The chance of getting a sample proportion of 70% or greater is 0.026.
Step-by-step explanation:
We are given that a poll shows that 50% of students play sports .
A random sample of 20 students showed that 70% of them play sports.
Let = sample proportion of students who play sports
The z-score probability distribution for the sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion of students who play sports = 70%
p = population proportion of students who play sports = 50%
n = sample of students = 20
Now, the chance of getting a sample proportion of 70% or greater is given by = P(
70%)
P(
70%) = P(
) = P(Z
1.95) = 1 - P(Z < 1.95)
= 1 - 0.97441 = <u>0.026</u>
The above probability is calculated by looking at the value of x = 1.95 in the z-table which has an area of 0.97441.
Hence, the chance of getting a sample proportion of 70% or greater is 0.026.