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Word Problem-ish: not very hard, just is to me.

Idaho Produce Corporation ships potatoes to its distributors in bags whose weights are normally distributed, with a mean of 50 pounds and a standard deviation of .5 pound. If a bag of potatoes is selected at random from a shipment, what is the probability that it weighs...

a.) More than 51 pounds

b.) Less than 49 pounds

c.) Between 49 and 51 pounds

This is Math 110 Finite Math at a college level. If anybody could help me with this problem, it would be amazing. Even if you only know how to do 1 of them. And if you do know how to do them, can you explain it to me too? Thanks so much.

P.S. If you are the same person who answered my last math question, you did a very good job, and i understand it now. So if you could help with this one too, i'd like that.

2 Answers

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  • Amy J
    Lv 6
    1 decade ago
    Favorite Answer

    a) You need to find a z-score for 51 pounds and find the area under the curve to the right of that z-score. This area is the probability of selecting a random bag that has that z-score or one more extreme, which is the same as weighing more than 51 pounds. You already know that the mean is 50, so μ = 50 and that the standard deviation is .5, so σ = 0.5

    z = (x - μ)/σ

    z = (51 - 50)/0.5

    z = 1/0.5

    z = 2

    Look at a z-table to find the area to the right of z = 2. P(z>2) = .0227 This is the probability that it weighs more than 51 pounds.

    b) Same idea, only you need to find a z-score for 49 pounds and find the area to the left of that z-score because you want less than 49 pounds instead of more than.

    z = (x - μ)/σ

    z = (49 - 50)/.5

    z = -1/.5

    z = -2

    Since the area to the left of -2 is the same as the area to the right of 2, look at a z-table to find the area to the right of z = 2. P(z>2) = .0227. Then P(z < -2) = .0227. This is the probability that it weighs less than 49 pounds (exactly the same as part a)

    c) The area under the entire curve is 1. You want the area between z = -2 and z = 2. You don't know that area yet, but you do know the area greater than 2 and less than -2. Subtract these from 1 to get the area inbetween.

    P(-2 < z < 2) = 1 - [P(z < -2) + P(z > 2)]

    P(-2 < z < 2) = 1 - [.0227 + .0227]

    P(-2 < z < 2) = 1 - .0454

    P(-2 < z < 2) = .9546

    This is the probability that it weighs between 49 and 51 pounds.

    Hope this helps you!

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