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Maurinko [17]
3 years ago
7

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

iversity are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent?
Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0

Answer: 0.1289

Step-by-step explanation:

Given : The proportion of all students at a large university are absent on Mondays. : p=0.15

Sample size : n=12

Mean : \mu=np=12\times0.15=1.8

Standard deviation = \sigma=\sqrt{np(1-p)}

\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369

Let x be a binomial variable.

Using the standard normal distribution table ,

P(x=4)=P(x\leq4)-P(x\leq3)              (1)

Z score fro normal distribution:-

z=\dfrac{x-\mu}{\sigma}

For x=4

z=\dfrac{4-1.8}{1.2369}\approx1.78

For x=3

z=\dfrac{3-1.8}{1.2369}\approx0.97

Then , from (1)

P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289    

Hence, the probability that four students are absent = 0.1289

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