The weights of the Imaginary Texas Winter Melon are normally

The weights of the Imaginary Texas Winter Melon are normally distributed with a mean of 20 pounds and a standard deviation of 4 pounds. Do the following exercises using anything from your notes and the table provided following all the questions Convert a weight of 26 pounds to a z-score. Convert a weight of 17 pounds to a z-score, Find the weight that corresponds to a z-score of z. Find the weight that corresponds to a z-score of -1.5. What percentage of these melons weighs between 16 and 24 pounds? What percentage of these melons weighs between 12 and 28 pounds? What percentage of these melons weighs between 8 and 32 pounds?

Solution

a)

Note that

z = (x-u)/sigma

Thus, if x = 26,

z = (26 - 20)/4 = 1.5 [ANSWER]

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b)

Again, by the same formula, if x = 17,

z = (17-20)/4 = -0.75 [ANSWER]

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c)

As

x = u + z*sigma

Then

x = 20 + 2*4 = 28 [ANSWER]

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d)

By the same formula,

x = u + z*sigma

Thus,

x = 20 + (-1.5)*4

x = 14 [ANSWER]

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