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DiKsa [7]
3 years ago
6

Yearly healthcare expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard devi

ation equal to $500. A sample of 36 families was selected and the mean and standard deviation were was found to be $3250 and $400 respectively. What is the probability of healthcare expenses in the population being greater than $4,000?
Mathematics
1 answer:
Misha Larkins [42]3 years ago
6 0

Answer:

The probability of healthcare expenses in the population being greater than $4,000 is 0.02275.

Step-by-step explanation:

We are given that yearly healthcare expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation equal to $500.

Let X = <u><em>yearly healthcare expenses of a family</em></u>

The z-score probability distribution for the normal distribution is given by;

                            Z  =  \frac{ X-\mu}{\sigma} }  ~ N(0,1)

where, \mu = population mean expense = $3,000

            \sigma = standard deviation = $500

Now, the probability of healthcare expenses in the population being greater than $4,000 is given by = P(X > $4,000)

     P(X > $4,000) = P( \frac{ X-\mu}{\sigma} } > \frac{4,000-3,000}{{500}{ } } ) = P(Z > 2) = 1 - P(Z \leq 2)

                                                                  = 1 - 0.97725 = <u>0.02275</u>

The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

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