I need someone to check my work for this normally distributed random variable question (Statistics)?

Question

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This is my work:

a) (50-42)/10 = 0.8 => z-value = 0.7881
   (32-42)/10 = -1 => z-value = 0.1587
   0.7881 - 0.1587 = 0.6294 = 62.94%

b) 10% = 0.1, corresponding z-value = 0.5398
   x = μ+zσ
   x = 42 + (-1.28)(10) = 29.1 = 29 months
c) n = 75
   (41-42)/(10/sqrt(75)) = -0.87 => z-value = 0.1922
   (40-42)/(10/sqrt(75)) = -1.73 => z-value = 0.0418
   0.1922 - 0.0418 = 0.1504

Answer 1

Note that the guarantee must be for less than $42$ months, for if it is for more than $42$ months then the company will be giving refunds for a majority of the batteries it sells.

For the standard normal $Z$, we have $\Pr(Z\le -1.28)\approx 0.1$. So the guarantee should be for about $42-(1.28)(10)$ months.

Remark: For the other two problems, the procedure is right. I have not checked the arithmetic.