Can you tell me how to solve this math/statistics problem?

It’s very straightforward. Once you know how to do it, you can accomplish many things.

First, the most important thing is the standard cumulative Normal distribution. With a normal distribution of mean 0 and stddev of 1, the value f(X) is the area under the curve from “negative infinity” to X. This in turn is the percentage of data points with a z-score below X, or in other words the percentage of points less than X.

Now, you must calculate the z-scores for the two points in question.
z-score = (X – mean)/stddev
(40 – 40)/5.5 = 0
(51 – 40)/5.5 = 2

Use a chart such as this to find the value of the cumulative distribution at those points. For 2, the value is .9772, and for 0 the value is 0.5.

p(40 < time < 51) = p(0 < z < 2) = p(z < 2) – p(z < 0) = 0.9772 – 0.5 = 0.4772

So, about 47.72% of people, or about 143 people, spend between 40 and 51 minutes.

They’re asking, How many people are between the mean and plus-two standard deviations (2-sigma)? Because 51 = 40 + 2 * 5.5

You know that in a normal distribution, plus or minus 2-sigma includes 95.5 percent of the population. Here it’s not plus-or-minus but mean to plus-2-sigma. By symmetry it’s half of the previous figure = 95.5/2 = 47.7%

Or look at this image that shows the desired portion as 34.1 + 13.6 = 47.7%

Finally, 47.7% of 300 people is 143.

Just to clarify, @gasman‘s approach is easiest when the z-scores involved are all integers, as they are in this problem. My approach takes a lot more work, but can be used for any z-scores.

@PhiNotPi Yes indeed. I figured when they give easy numbers they must be sticking to basics. In general it’s more complicated & requires your method.

I am unfortunately probably too late to help, but for what it is worth, here is how you expand Pascal’s triangle.
Start with:

11

To get the second row, bring down the 1 on left and, moving left to right add each successive pair of elements, and then bring down the one on the right to get:
1(1+1)1 or 121. The next row is 1(1+2)(2+1)1 or 1331.
To interpret this in terms of binomial expansion, the nth row is the coefficients for the polynomial (a+b)^n. The third row gives us (a+b)^n = a^3 + 3a^2b + 3ab^2 + b^3. In each case, start with a^n. As you go from one term to the next, decrease the exponent of a by 1 and increase the exponent of b by1. The two exponents will add to n for each term.

Best of luck on the test!