Statistics r105 M&W

Question

A particular fruit's weights are normally distributed, with a mean of 259 grams and a standard deviation of 12 grams.

If you pick one fruit at random, what is the probability that it will weigh between 234 grams and 275 grams?

Enter at least 3 decimal places.

Answer 1

mu = 259

sigma = 12

z_low = (234 - mu)/sigma

z_high = (275 - mu)/sigma

z_low = -2.083333

z_high = 1.333333

P(z_low < z < z_high) = [P(z < 1.333) - P( z < -2.083)] = 89.01%

You can get those probabilities from a table or a calculator; which ever you are using.

Answer 2

You could complete this problem by hand, using the appropriate formula and Z-table, or in the calculator.

Using the formula, z = (x-μ)/ο, you will have to find the z-scores that represent each data value (x₁ = 234 and x₂ = 275). Afterward, you would use the z-table to find the probabilities associated with each z-score. Because you are looking for the probability between the two data values, you would subtract the biggest and smallest probabilities you get.

I hope this helps. If I knew what calculator you were using, I can give you the appropriate steps to work out this answer.