4. The compressive strength of cement is assumed to be normally distributed with a mean of 8000 kilograms per sq cm and a standard deviation of 200 kilograms per sq. cm.
a) Find the probability that the strength is less than 8200 kg per sq. cm
b) Find the probability that the strength is between 7500 and 7700 kg per sq. cm
c) Determine the value for which the probability that the strength of cement is below this value is 90%.

3. In a study for Health Statistics, it was found that the mean height of female 20-25 years old was 64.1 inches. If height is normally distributed with a standard deviation of 2.8 inches.
a) Determine the height required to be in the top 10% of all 20-25 years old females.
b) A “one-size-fits all” robe is being designed that should fit 90% of 20-25 years old females; what heights constitute the middle 90% of all 20-25 years old females?

2. The time it takes a student to cycle to school is normally distributed with a mean of 15 minutes and a variance of 2. The student has to be at school at 8.00a.m. At what time should the student leave her house so that she will be late only 4% of the time?

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In general, you first need to define a variable, say... X.

Let X be [... ]

Then,

Then you work out the z value of the X you're looking for using and look up in the table to get the probability. It is advised to make a sketch for each probability you're looking for to make sure you get the correct probability.

Post what you've come up with so far :)

I realize this has nothing to do with your question, but that's some seriously strong cement! A typical compressive strength value for concrete is more like 250 kg/cm^2. Cement (which is not the same as concrete) is generally less than that, as far as I know.

As for your question, Unknown already told you exactly what you need to do.