Question

The mean amount spent by a family of four on food per month is $507 with...

The mean amount spent by a family of four on food per month is $507 with a standard deviation of $73. Assuming that the food costs are normally distributed.

a. what is the probability that a family spends less than $406 per month? Give your answer to 4 decimals.

b. what is the probability that a family spends at least $711 per month? Give your answer to 4 decimals.

Math   Statistics-And-Probability   
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Answer #1

Define random variable X : Food costs

X is normally distributed with Mean = and

Standard deviation =

a) Here we have to find P(X < 406)

   where z is standard normal variable

= P(z < -1.38) (Round to 2 decimal)

= 0.0838 (From statistical table of z values)

Probability that a family spends less than $406 per month is 0.0838

b)

Here we have to find

   (Round to 2 decimal)

= 1 - P(z < 2.79)

= 1 - 0.9974 (From statistical table of z values)

= 0.0026

Probability that a family spends at least $711 per month is 0.0026

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