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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.
