Question

In a small town, 50% of single family homes have a front porch. 48 single family homes are randomly selected. Let X represent the number of single family homes with a porch. What normal distribution best approximates X?

Answer 1

Answer:

N(24, 3.46)

Step-by-step explanation:

We are given the following in the question:

Percentage of family homes having front poach = 50%

$p = 50\% = 0.50$

Sample size, n = 48

Normal approximation to the given distribution:

$\mu = np = 48(0.50) = 24$

$\sigma = \sqrt{np(1-p)} = \sqrt{48(0.50)(1-0.50)} = 3.46$

Thus, the distribution of single family homes is best approximated by the normal distribution N(24, 3.46) where mean is 24 and standard deviation is 3.46