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.

Complete Question

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The mean of p is

The standard deviation is  

The probability is  

Step-by-step explanation:

From the question

        The proportion of those with IQ over 100 is  p

        The selected sample is  

From the question the mean is of p is

The standard deviation is  

We are asked to determine

By applying normal approximation

       →    

Where  

             = 0.6

  So the the probability is  

We can also look at this probability in this manner

From the z table z value of 0.8 is  0.78814

blue marble is 15 times out of 50 = 15/50 reduces to 3/10

landing on tails is 24 out of 50 = 24/50 reduces to 12/25

to find the probability of both multiply together:

3/10 x 12/25 = 3 x 12 / 10 x 25 = 36/250

if you multiplied the numerator and denominator by 10 you get 360/2500.

the answer is 360/2500