Probability question

Question

A particular fruit's weights are normally distributed, with a mean of 510 grams and a standard deviation of 11 grams.

If you pick one fruit at random, what is the probability that it will weigh between 528 grams and 529 grams

Answer 1

let x = fruit weight, want to find P(528 < x < 529)

x is N(510,11)

transform limits to x in above inequality to standard normal (z) which is N(0,1) by subtracting mean and dividing by standard deviation:

P(528 < x < 529) = P( (528-510)/11 < z < (529-510)/511) = P(1.64 < z < 1.73) = P(z < 1.73) - P(z < 1.64) = 0.9582 - 0.9485 = 0.0097