How would i figure out the normal distribution for problem below?

Question

1.    The cafeteria sells delicious pomegranates, and sells them using the catchy slogan “Normally Distributed Pomegranates.” You see, the number of arils (seeds) in the pomegranates is normally distributed, with a m = 34.2 and s = 2.53. They guarantee it, or you get a free cookie! Draw a sketch for each part.

a)    You buy a pomegranate and in the process of eating it discovers that is contains only 23 seeds. What are the chances of getting 23 or less seeds in a pomegranate?

b)    The person behind you in line really, really wants to get a pomegranate that has 33 to 43 seeds in it, no more, no less. What is the probability that she gets what she wants?

c)    Suppose you refuse to eat any pomegranate that is in the bottom 12% of the distribution. How many seeds must be in a pomegranate before you’ll eat it?

I have attempted this problem numerous times and remain stumped. My math for a) is 23-34.2/2.53= the z value of -4.42687747. I used stat disk to find the cumu area but it just says 1.00000. I dont understand what the means or why its saying that.

Answer 1

The z-score is the number of standard deviations the data value differs from the mean. The probability of the data value being 3 SD below the mean is only 0.0013. The probability of the data value being -4.42 standard deviations below the mean is so small, most tools will provide a probability of zero. You're getting a probability of 1 means you did not utilize your tool correctly.