Question

A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of people who grew up as the only child. She finds that of them have an IQ score over . It is known that of the general population has an IQ score exceeding . Find the mean of , where is the proportion of people with IQ scores over in a random sample of people. Find the standard deviation of . Compute an approximation for , which is the probability that there will be or more individuals with IQ scores over in a random sample of . Round your answer to four decimal places.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Complete Question

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Answer:

The mean of p is $\mu = 0.5$

The standard deviation is  $\sigma = 0.025$

The probability is  $P(p \ge 0.52) = 0.2119$

Step-by-step explanation:

From the question

        The proportion of those with IQ over 100 is  p

        The selected sample is  $n =400$

From the question the mean is of p is

              $\mu = 0.50$

The standard deviation is  

             $\sigma = \sqrt{\frac{p(1-p)}{n} }$

                 $= \sqrt{\frac{0.5 *0.5}{400} }$

                $= 0.025$

We are asked to determine

      $P(\r p \ge 0.52)$

By applying normal approximation

    $P(\= p \ge 0.52 )$    →    $P(Z \ge z)$

Where  $z = \frac{x - \mu}{\sigma}$

          $z = \frac{0.52-0.5}{0.025}$

             = 0.6

  So the the probability is  

 $P(Z \ge 0.8)$

We can also look at this probability in this manner

                   $P(Z \ge 0.8) = 1- P(Z < 0.8)$

From the z table z value of 0.8 is  0.78814

                                      $P(Z \ge 0.6)=1- 0.78814$

                                                         $= 0.2119$