Question

A town has 685 households. the number of people per household is normally distributed with a mean, x, of 3.67 and a standard deviation , x, of .34. approximately how many households have between 2.99 and 4.01 people

Answer 1

Using the z-score calculation for a normal distribution, approximately 561 households in the town have between 2.99 and 4.01 people.

Step-by-step explanation:

To determine approximately how many households have between 2.99 and 4.01 people, we use the standard normal distribution and z-scores. First, we calculate the z-scores for 2.99 and 4.01 using the provided mean (μ = 3.67) and standard deviation (σ = 0.34). The z-score formula is z = (X - μ) / σ.

For 2.99: z1 = (2.99 - 3.67) / 0.34 = -2
For 4.01: z2 = (4.01 - 3.67) / 0.34 = 1

Next, we consult the standard normal distribution table to find the probabilities corresponding to these z-scores. The cumulative probability for z1 = -2 is approximately 0.0228, and for z2 = 1 is approximately 0.8413. To find the probability that a household has between 2.99 and 4.01 people, we subtract the probability at z1 from the probability at z2:

P(2.99 < X < 4.01) = P(z2) - P(z1) = 0.8413 - 0.0228 = 0.8185

Therefore, about 81.85% of the households have between 2.99 and 4.01 people. To find the number of households, we multiply this percentage by the total number of households in the town:

Number of households = Total households × P(2.99 < X < 4.01)
Number of households = 685 × 0.8185 ≈ 561

Approximately 561 households have between 2.99 and 4.01 people.

Answer 2

Hello there!!

Let us solve this problem, shall we?

First: You need to solve the 685 divided by 3.67.
Second: You find out the devidation
When you do all the steps: THE ANSWER IS 11!!!!!