Atravel agency did a survey and found that the average local family spends $1900 on a summer vacation. the distribution is normally distributed with standard deviation $390. a. what percent of the families took vacations that cost under $1500. round to the nearest percent.

The percentage is 15%

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The average local family spends $1900 on a summer vacation

- The distribution is normally distributed with standard deviation $390

- We need to find what percent of the families took vacations that

 cost under $1500

∵ The mean is $ 1900

∴ μ = 1900

∵ The standard deviation is $390

∴ σ = 390

∵ The vacation cost is under $1500

∴ x = 1500

∵ z-score = (x - μ)/σ

- Substitute the values above in the rule

∴ z-score = (1500 - 1900)/390 = -1.0256

- Lets use the normal distribution table of z

∵ P(z < 1500) = 0.1515

∵ P(x < 1500) = P(z < 1500)

∴ P(x < 1500) = 0.1515

∴ The percentage of the families took vacations that cost under

  $1500 is ⇒ 0.15 × 100% = 15%

∴ The percentage is 15%

just needed some points but try socratic

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: