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The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $425 per month?​

Answer :

Answer:

[tex] z=\frac{x- \mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{425-500}{75}= -1[/tex]

And we can calculate this probabilit using the normal standard distribution or excel and we got:

[tex] P(z<-1)= 0.159[/tex]

Step-by-step explanation:

If we define the random variable of interest "the amount spent by a family of four of food per month" and we know the following parameter:

[tex] \mu = 500, \sigma = 75[/tex]

And we want to find the following probability:

[tex] P(X<425)[/tex]

And we can use the z score formula given by:

[tex] z=\frac{x- \mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{425-500}{75}= -1[/tex]

And we can calculate this probabilit using the normal standard distribution or excel and we got:

[tex] P(z<-1)= 0.159[/tex]

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