<u></u><u>The correct answer is 47.5%, or 0.475.</u>
Explanation:
The empirical rule states that in any normal distribution:
68% of data will fall within 1 standard deviation of the mean;
95% of data will fall within 2 standard deviations of the mean; and
99.7% of data will fall within 3 standard deviations of the mean.
The mean is 500 and the standard deviation is 100. This means that 700 is 2 standard deviations away from the mean:
(700-500)/100=200/100=2.
We know that 95% of data will fall within 2 standard deviations from the mean. However, included in the 95% is data less than the mean and greater than the mean. Since we are only concerned with the scores from 500 to 700, we only want the half that is greater than the mean:
95/2 = 47.5%, or 0.475.
#1 is 4
#2 is 9
#3 is 16
#4 can't read the numbers
Answer:
The probability that 75% or more of the women in the sample have been on a diet is 0.037.
Step-by-step explanation:
Let <em>X</em> = number of college women on a diet.
The probability of a woman being on diet is, P (X) = <em>p</em> = 0.70.
The sample of women selected is, <em>n</em> = 267.
The random variable thus follows a Binomial distribution with parameters <em>n</em> = 267 and <em>p</em> = 0.70.
As the sample size is large (n > 30), according to the Central limit theorem the sampling distribution of sample proportions (
) follows a Normal distribution.
The mean of this distribution is:

The standard deviation of this distribution is: 
Compute the probability that 75% or more of the women in the sample have been on a diet as follows:

**Use the <em>z</em>-table for the probability.

Thus, the probability that 75% or more of the women in the sample have been on a diet is 0.037.