Question

Distribution of ProportionsEach week, Nielsen Media Research conducts a survey of 5000 households and records the proportion of households tuned to 60Minutes. If we obtain a large collection of those proportions and construct a histogram of them, what is the approximate shape of the histogram?

Short answer

The histogram will be bell-shaped.

Step-by-step solution

Given information

A survey consisting of 5000 households is conducted. The proportion of households that watch “60 Minutes” is recorded.

Sampling distribution of sample proportions

Using the central limit theorem, it is known that the distribution of the sample proportions is normally distributed. Since the distribution of sample proportions is normally distributed, the histogram of such proportions would be bell-shaped.

Here, the sample proportion of households that watch “60 Minutes: is recorded.

A large collection of such sample proportions is considered.

Thus, the distribution of the sample proportion of households that watch “60 Minutes” will be normal. The histogram of such proportions will be bell-shaped.