Question

PLEASE HELPPPP

A standard I.Q. test produces normally distributed results with a mean of 100 and a standard deviation of 15 for the city of New York. Out of approximately 8,400,000 citizens, how many of these people would have I.Q.s below 67?

Answer 1

Approximately 210,000 people in New York City are expected to have an IQ below 67, as this is more than two standard deviations below the mean IQ of 100, and IQs are normally distributed.

Step-by-step explanation:

To determine how many people in New York City have IQs below 67, we can utilize the properties of the normal distribution. An IQ of 67 is more than two standard deviations below the mean since each standard deviation is 15 points and the mean is 100. According to the empirical rule (or 68-95-99.7 rule), approximately 95% of the data within a normal distribution falls within two standard deviations of the mean. That means 2.5% of the distribution is below this range, as the distribution is symmetric, and 2.5% is above the two standard deviation range on the higher side.

The population of New York City is approximately 8,400,000 individuals. To find how many have IQs below 67, we calculate 2.5% of this population:

2.5% of 8,400,000 = 0.025 * 8,400,000

2.5% of 8,400,000 = 210,000

Therefore, around 210,000 people in New York City are expected to have an IQ below 67.

Answer 2

approx 193200

Step-by-step explanation:

As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s ( where s is a standard deviation)

So the border is 100+-2*15=70 and that is approx=67.

95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons

So the residual number of the citizens =8400000-8013600=386400 citizens

Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.

N=386000/2=193200