Question

temperatures in june in the paradise city are distributed nearly normally with mean 76 degrees and standard deviation 6 degrees f. which of the following temperatures would be considered unusual?
○ 89.2
○ 77.8
○ 68.8
○ 74.2
○ 80.2

Explanation:

Step1: Recall the concept of unusual values

In a normal distribution, values that are more than 2 standard deviations away from the mean are considered unusual. The formula for the range of usual values is \(\mu - 2\sigma\) to \(\mu + 2\sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Given \(\mu = 76\) and \(\sigma = 6\).

Step2: Calculate the lower and upper bounds

First, calculate the lower bound: \(\mu - 2\sigma=76 - 2\times6 = 76 - 12 = 64\)

Then, calculate the upper bound: \(\mu + 2\sigma=76+2\times6 = 76 + 12 = 88\)

Step3: Check each temperature

• For 89.2: \(89.2>88\), so it is outside the range of usual values.
• For 77.8: \(64<77.8<88\), so it is usual.
• For 68.8: \(64<68.8<88\), so it is usual.
• For 74.2: \(64<74.2<88\), so it is usual.
• For 80.2: \(64<80.2<88\), so it is usual.

Answer:

89.2