Posted by Steven on Monday, December 16, 2013 at 12:53pm.
A manufacturing facility produces iron rods whose mean diameter is 2.5 inches with a standard deviation of 0.2 inch. If a sample of 50 metal rods produced by the facility were randomly selected, what is the probability that the mean of these rods will lie between 2.4 inches and 2.8 inches?
According to census statistics, Hispanics comprise 27.5% of the population of New York City. Suppose a random sample of 400 people is selected from New York City. What is the probability that there are fewer than 22% of Hispanics in the sample? Hint: Use Normal approximation to the Binomial distribution.

Statistics  MathGuru, Monday, December 16, 2013 at 6:46pm
Use zscores.
First problem:
z = (x  mean)/(sd/√n)
Find two zscores:
z = (2.4  2.5)/(0.2/√50) = ?
z = (2.8  2.5)/(0.2/√50) = ?
Finish the calculations.
Next, check a ztable to find the probability between the two scores.
Find mean and standard deviation.
mean = np = 400 * .275 = ?
standard deviation = √npq = √(400 * .275 * .725) = ?
Note: q = 1  p
Finish the calculations.
Next, use zscores:
z = (x  mean)/sd
z = (.22  mean)/sd
Substitute the mean and standard deviation into the zscore formula and calculate, then use a ztable to find the probability.
I hope this will help get you started.

Statistics  MathGuru, Monday, December 16, 2013 at 6:48pm
Note: For the second problem, we use the normal approximation to the binomial distribution when finding the mean and standard deviation.

Statistics  Steven, Tuesday, December 17, 2013 at 7:09pm
How would you check the Z table for the first problem?
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