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sertanlavr [38]
3 years ago
11

The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming that the food cos

ts are normally distributed, what is the probability that a family spends less than $410 per month?
Mathematics
1 answer:
JulijaS [17]3 years ago
6 0

Answer:

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given mean of the population = 500 </em>

<em>Given standard deviation of the Population = 75</em>

Let 'X' be the variable in normal distribution

      Z = \frac{x-mean}{S.D}

<em>Given X = $410</em>

<em></em>Z = \frac{410-500}{75} = - 1.2<em></em>

<u><em>Step(ii):-</em></u>

The probability that a family spends less than $410 per month

P( X < 410) = P( Z < - 1.2 )

                  =  0.5 - A( -1.2)

                 = 0.5 - A(1.2)

                = 0.5 - 0.3849  ( ∵from normal table)

                = 0.1151

<u>Final answer:-</u>

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

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