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AfilCa [17]
3 years ago
13

A bottle maker believes that 14% of his bottles are defective. If the bottle maker is accurate, what is the probability that the

proportion of defective bottles in a sample of 622 bottles would be less than 11%
Mathematics
1 answer:
Hitman42 [59]3 years ago
4 0

Answer:

z = \frac{0.11-0.14}{0.0139} = -2.156

And we can use the normal standard distribution table and we got:

P(Z

Step-by-step explanation:

For this case we know the following info given:

p =0.14 represent the population proportion

n = 622 represent the sample size selected

We want to find the following proportion:

P(\hat p

For this case we can use the normal approximation since we have the following conditions:

i) np = 622*0.14 = 87.08>10

ii) n(1-p) = 622*(1-0.14) =534.92>10

The distribution for the sample proportion would be given by:

\hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}})

The mean is given by:

\mu_{\hat p}= 0.14

And the deviation:

\sigma_{\hat p}= \sqrt{\frac{0.14*(1-0.14)}{622}}= 0.0139

We can use the z score formula given by:

z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}

And replacing we got:

z = \frac{0.11-0.14}{0.0139} = -2.156

And we can use the normal standard distribution table and we got:

P(Z

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