Statistics - Standard Deviation and Probabilities.

1)Assume x is normally distributed with mean u=15 and standard deviation 0=3. Use the approximate areas beneath the normal curve, as discussed in this section, to answer the following questions. Find p(x<_9)

2)Your high school graduating class had 564 members. Thirty-three percent of these are expected to attend college. The probability that less than 160 will attend college is

3)In your college campus, 30% of the students use tobacco in some form. In your statistics class of 40 students, the probability of finding at least 15 students who use tobacco is

4)Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals:

5)If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be:

these problems are the only ones I got wrong on my test. I do not understand what I did wrong, the problems that were simular were correct. Please help me.

Solution Preview

(1) m = 15, s = 3, x = 9

z = (x - m)/s = (9 - 15)/3 = -2

P(x <= 9) = P(z <= -2) = 0.023

(2) n = 564, p = 0.33, q = 1 - p = 0.67, x = 160

m = np = 564 * 0.33 = 186.12 and s = sqrt(npq) = ...

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