Question

multiple choice 2 points
which of the following data - sets is least likely to be a normal distribution?
the growth of a bacteria population
shoe sizes of adult females
iq scores
numeric 2 points
given a normally distributed data set with the mean = 80 and the standard deviation = 8
below 64?

Explanation:

• The growth of a bacteria population: Bacterial growth often follows an exponential pattern (e.g., \(P(t)=P_0e^{rt}\) where \(P(t)\) is the population at time \(t\), \(P_0\) is the initial population, and \(r\) is the growth rate). It is not a normal distribution.
• Shoe sizes of adult females: Shoe - size data may have some skew (e.g., there are limits to how small or large shoe sizes can be in a practical sense, and the distribution may not be symmetric around a central value in the same way as a normal distribution).
• IQ scores: IQ scores are designed to be normally distributed. The mean of a standard IQ test is often set to 100 (but in some cases, if re - scaled, could be adjusted), and the standard deviation is 15. However, if we assume a different scaling, and given the properties of normal distributions (symmetric, bell - shaped curve), IQ scores are a classic example of a variable that is approximately normally distributed.

Answer:

IQ scores