To win a prize, the diameter of a tomato must be greater than 4 in. The diameters of a crop of tomatoes grown in a special soil are normally distributed, with a mean of 3.2 in. and a standard deviation of 0.4 in. What is the probability that a tomato grown in the special soil will be a winner? I know the answer is 2.5 but I don't know how to get that.

Question

To win a prize, the diameter of a tomato must be greater than 4 in. The diameters of a crop of tomatoes grown in a special soil are normally distributed, with a mean of 3.2 in. and a standard deviation of 0.4 in. What is the probability that a tomato grown in the special soil will be a winner?  I know the answer is 2.5 but I don't know how to get that.

mrnood · Answer

the answer cannot be 2.5 - a probability is normally expressed as a value between 0 and 1 (or sometimes as a percentage)

You are obviously studying the normal distributin curve and Standard deviation.

The curve has the property that you can know the probability of a number being a certain distance from the mean, when that number is expressed in Standard deviations.

We know the menan value is 3.2 in and the SD is 0.4in

we are looking for a tomato greater than 4 inches

4 inches is 0.8 in more than the mean. How many times the SD is this?

mrnood · Answer

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