# The daily temperature in New York City in July are normally distributed with a mean of 18 C and a standard deviation of 1.5 C. Determine the probability (or chance) of the temperature tommorow...

The daily temperature in New York City in July are normally distributed with a mean of 18 C and a standard deviation of 1.5 C. Determine the probability (or chance) of the temperature tommorow being under 15 degrees AND between 16 and 16.5 degrees.

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### 1 Answer

The daily temperature in New York City in July are normally distributed with a mean of 18 degrees C and a standard deviation of 1.5 C. The temperature on any day cannot be under 15 C AND between 16 and 16.5, it is either below 15 C OR between 16 C and 16.5 ,

To determine the probability of the temperature in this range find the z-score for each of the values.

The z score for a value x is given by `(x - mu)/sigma`

15 C : (15 - 18)/1.5 = -2

16 C : (16 - 18)/1.5 = -1.33

16.5 C: (16.5 - 18)/1.5 = -1

Using a normal distribution table the value of the area below -2 is 0.0228. And the area between -1.33 and -1 is (0.1587 - 0.0918) = 0.0669. Adding the two, the probability that the temperature is less than 15 C or between 16 C and 16.5 C is 0.0897.

**There is a 8.97% probability that the temperature lies under 15 C or between 16 C an 16.5 C.**

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