Question

In the U.S., 95% of children have received their DTaP vaccine. Calculate the probability that fewer than 700 out of a sample of LaTeX: n = 750n=750 children received their DTaP vaccine.

Answer 1

Answer:

0.0183

Step-by-step explanation:

The percentage of students, who received their DTaP vaccine is 95%.

This implies that:

$p = 0.95$

and

$q = 1 - 0.95 = 0.05$

The standard deviation of the proportion is

$= \sqrt{ \frac{pq}{n} }$

$= \sqrt{ \frac{0.95 \times 0.05}{750} } \\ = 0.00796$

We want to find the probability, that the sample proportion,

$\hat p \leqslant \frac{700}{750} \\ \hat p \leqslant 0.9 \bar3$

$P(\hat p\le0.9\bar3)=P(Z\le \frac{0.9 \bar3 - 0.95 }{0.00796} ) \\ = P(Z\le - 2.09) \\ = 0.0183$