Answer:
Probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is 0.0688.
Step-by-step explanation:
We are given that a survey of students at a large university found that 82% had purchased textbooks from an off-campus vendor at least once during their college career.
Also, 45 students are randomly sampled.
<u><em>Let </em></u><u><em> = sample proportion of students who have purchased textbooks from an off-campus vendor at least once during their college career.</em></u>
The z-score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion = = 0.89
p = population proportion of students who had purchased textbooks from an off-campus vendor at least once during their college career = 82%
n = sample of students = 45
Now, probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is given by = P( 0.89)
P( 0.89) = P( ) = P(Z 1.50) = 1 - P(Z < 1.50)
= 1 - 0.9332 = <u>0.0688</u>
<em>The above probability is calculate by looking at the value of x = 1.50 in the z table which ha an area of 0.9332.</em>
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Therefore, the required probability is 0.0688.