Question

Z-scores can be used to assess whether data values in a certain distribution are unusual. This is appropriate when the data distribution is approximately bell-shaped. The National Oceanic and Atmospheric Administration (NOAA) reports that, from 1971 to 2000, July average temperatures in West Central Indiana had a mean of 74.5°F with a standard deviation of 2.0°F.^‡

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1. Is it reasonable to assume that July average temperatures in West Central Indiana from 1971 to 2000 follow a bell-shaped distribution? Explain.

Answer 1

From the given information,

From 1971 to 2000, there will be 30 entries for july average temperatures which is sufficiently large and hence by using central limit theorem,

We can conclude that,

It follow a bell-shaped distribution.

Thank you.