Question

Suppose 80% of Grade 12 students bring their mobile phone to school. A random sample of 50 Grade 12 students was randomly selected.

a) Provide a description of the most appropriate statistic. [2]


b) Identify the sampling distribution of the statistic defined previously. [4]
Note: Please note that checking condition is part of the procedure.


c) Find the probability that more than 70% of the random sample of 50 Grade 12 students who bring their mobile phone to school.

Answer 1

The most appropriate statistic is a sample proportion. The sampling distribution of the sample proportion can be approximated by the normal distribution. To find the probability, calculate the mean and standard deviation of the sample proportion and use the cumulative distribution function of the normal distribution.

Step-by-step explanation:

a) The most appropriate statistic to describe this situation is a sample proportion. A sample proportion is used to estimate the population proportion, which in this case is the proportion of Grade 12 students who bring their mobile phone to school.

b) The sampling distribution of the sample proportion can be approximated by the normal distribution, under certain conditions, namely if the sample size is large enough and the sampling is done randomly. This is known as the normal approximation to the binomial distribution.

c) To find the probability that more than 70% of the random sample of 50 Grade 12 students bring their mobile phone to school, we can use the normal distribution approximation. First, calculate the mean and standard deviation of the sample proportion using the sample size and population proportion. Then, use the cumulative distribution function of the normal distribution to find the probability.