Question

The total energy need during pregnancy is normally distributed, with a mean of 2600 kcal/day and a standard deviation = 50 kcal/day. What is the probability that a randomly selected pregnant woman has an energy need of more than 2615 kcal/day?

This problem is whooping my butt and I could really use some help with finding the steps to solve these types of problems!

Answer 1

Hi there. Do you know what a z-score is, or a z-score table?

Answer 2

I just started using z-scores and tables, but I'm still a bit fuzzy with them.

Answer 3

OK, well, the basic idea of a z-score is it describes a number of standard deviations above the mean or below

Answer 4

so if the standard deviation is 10, and you have something 50 above the mean, it has a z-score of 5. if it's 100 above the mean, it has a z-score of 10. does that make sense so far?

Answer 5

So basically I want to find the z-score and use that with the z-table?

Answer 6

yes. a z-score table tells you the probability that a number selected at random from a normal distribution will be below that z-score.

Answer 7

for example, a z-score of 0 means 0 standard deviations above the mean -- that is, equal to the mean -- so in a z-score table, the z-score of 0 is listed as 0.5000, i.e. there's an equal probability of a random sample being above the mean or below the mean.

Answer 8

Thank you so much. My prof didnt really go over this in depth at all yesterday and i've been totally lost.

Answer 9

In a z-score table, a z-score of 1 is listed as 0.8413, which means there's an 84.13% chance that a random normally distributed number will be at most 1 standard deviation above the mean. and, conversely, that (1-0.8413) or a 15.87% chance that the number will be more than 1 standard deviation above the mean.

Answer 10

I'm looking up the formula to find the z-score and a table now.

Answer 11

As you go further and further to the right of a bell-shaped curve, more and more of the mass is to your left, i.e. there's a higer and higher probability that a number selected at random will be at or below the z-score entry you're looking at.

Answer 12

So for example, going to a z-score of 4 -- 4 standard deviations above the mean -- is quite rare. The z-score table tells you 0.999968, meaning there's a 99.9968% chance that a number (selected at random from a normal distribution) will be less than 4 standard deviations above the mean.

Answer 13

So in any case, your job is to convert the problem into a z-score table lookup. Let's return to it. Mean is 2600, std dev is 50, and they want to know the probability that it's 2615 or higher. So how far above the mean is 2615, and how many standard deviations is that?

Answer 14

I think im starting to get it. So z = (x - \[\mu\])/\[\sigma\]

Answer 15

(sorry that formatting is out of wack)

Answer 16

yeah, that's the formula, i just want to make sure you understand what it actually means. the z-score counts how many standard deviations above the mean we've gone. If the mean is 100, and the standard deviation is 10, then 100 has a z-score of 0, 110 has a z-score of 1, 120 has a z-score of 2, etc.

If the mean is 0 and the std dev is 50, then a z-score of 0 is 0, z-score of 1 is 50, z-score of 2 is 100, z-score of 3 is 150, etc.

Answer 17

z-scores can be negative, too. If the mean is 100 and std dev is 10, then a z-score of -1 is 90, of -2 is 80, of -3 is 70, etc.

Answer 18

So what the formula does is first find how far above the mean we are, then divide by standard deviation to count how many standard deviations that is.

Answer 19

How does the reading on the z-table change if the number of standard deviations from the mean is negative?

Answer 20

the z-table only tells you how much of the mass of the bell curve is to your left. So as you go to positive z-scores, it gets very large. and as you go to negative z scores, it gets very small.

Since the bell curve is symmetrical, this property holds: the table for a z score of -3 (to pick a number as an example) will be the same as 1 - (table for z=+3). in other words, the table at Z=+3 tells you everything to the left, which is 1 minus the little tail that's to your right. That's exactly the same as the little tail piece that's to your left at -3.

Answer 21

You can find this in the table you're looking at. The entry for -1 says 0.1587. The entry for +1 says 0.8413. Note that 0.1587 is equal to (1 - 0.8413). In other words, the probability that you'll be 1 standard deviation below the mean is the same as the probability you'll be one standard deviation above the mean.