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Standard Deviation, Probability

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Suppose the probability distribution for the high temp in Nevada on June 1 is normally distributed with a mean of 65 degrees. If a box plot was made it would have an IQR = 20 degrees.

1. What's the standard deviation of that probability distribution?
I know the answer is 20 / 1.35 - where do you come up with the 1.35?

2. Find the probability that June 1sts temp is in the 70s.

3. If the high temp for June 1, 2, 3 all have the same probability distribution and are statistically independent, what's the probability that high temps for that period will be in the 70s every day?

Please show your work so I can follow how you determined the answers.

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A complete, neat and step-by-step solution is provided below. The posting helps find standard deviation, probability, and probability distributions.

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(1) What's the standard deviation of that probability distribution?

We have the following formula for calculating the SD of a data set when the IQR is known:

SD = IQR/1.35

So, SD = 20/1.35 ...

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