Question

A politician claims that 20% of the millions of votes cast for his opponent are fraudulent. To test this claim, an investigator collects a random sample of 90 ballots and contacts the voters whose names appear on the ballots to determine if each ballot is in fact fraudulent. Use a normal approximation to find the probability that less than 10 of the selected ballots turn out to be fraudulent, assuming the politician's claim is correct.

Answer 1

Answer:

"0.0125" is the right solution.

Step-by-step explanation:

The given values are:

Random sample,

n = 90

Claims,

p = 20%

or,

  = 0.20

By using normal approximation, we get

⇒  $\mu = np$

On substituting the values, we get

⇒      $=90\times 0.20$

⇒      $=18$

Now,

The standard deviation will be:

⇒  $\sigma=\sqrt{np(1-p)}$

On putting the above given values, we get

⇒      $=\sqrt{90\times 0.20\times (1-0.20)}$

⇒      $=\sqrt{18\times 0.8}$

⇒      $=\sqrt{14.4}$

⇒      $=3.7947$

hence,

By using the continuity correction or the z-table, we get

⇒  $P(x < 10) = P(x < 9.5)$

⇒  $P(x < 10) = P(\frac{x-\mu}{\sigma} -\frac{9.5-18}{3.7947} )$

⇒  $P(x < 10) = P(Z < -2.24)$

From table,

⇒  $P(x < 10) = 0.0125$