Answer:
0.3137 is the probability that more than 100 students will pass the college placement exam.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 151
probability student will pass their college placement exam = 64%
[tex]p = 0.64[/tex]
Formula:
[tex]\mu = np = 151(0.64) = 96.64\\\sigma = \sqrt{np(1-p)} = \sqrt{151(0.64)(1-0.64)} = 5.89[/tex]
We have to evaluate
P(x > 100)
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]P( x > 100) = P(100-0.5) = P( z > \displaystyle\frac{99.5 - 96.64}{5.89})\\\\ = P(z > 0.4855)[/tex]
[tex]= 1 - P(z \leq 0.4855)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x >99.5) = 1 - 0.6863 =0.3137 = 31.37\%[/tex]
0.3137 is the probability that more than 100 students will pass the college placement exam.
