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Answer:
The probability that less than 800 students who said they still had their original major is 0.50 or 50%.
Step-by-step explanation:
Let the random variable <em>X</em> be described as the number of third-year college students if they still had their original major.
The probability of the random variable <em>X</em> is, P (X) = <em>p</em> = 0.50.
The sample selected consisted of <em>n</em> = 1600 third-year college students.
The random variable <em>X </em>thus follows Binomial distribution with parameters n = 1600 and p = 0.50.
As the sample size is large, i.e.<em>n</em> > 30, and the probability of success is closer to 0.50, Normal approximation can be used to approximate the binomial distribution.
The mean of <em>X</em> is:
The standard deviation of <em>X</em> is:
It is provided that Picky Polls got less than 800 students who said they still had their original major.
Then the probability of this event is:
**Use the <em>z</em>-table for the probability.
Thus, the probability that less than 800 students who said they still had their original major is 0.50.
