Respuesta :
Answer:
95% of monthly food expenditures are between $110 and $190.
Step-by-step explanation:
Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.
To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?
Solution :
At 95% of the data is between two standard deviation to left and right of the mean is given by,
To the left side, [tex]\bar{x}-2\sigma[/tex]
To the right side, [tex]\bar{x}+2\sigma[/tex]
We have given,
The sample mean [tex]\bar{x}=\$150[/tex]
The standard deviation [tex]\sigma=\$20[/tex]
Substitute in the formula,
[tex]\bar{x}-2\sigma[/tex]
[tex]=150-2(20)[/tex]
[tex]=150-40[/tex]
[tex]=110[/tex]
[tex]\bar{x}+2\sigma[/tex]
[tex]=150+2(20)[/tex]
[tex]=150+40[/tex]
[tex]=190[/tex]
Therefore, 95% of monthly food expenditures are between $110 and $190.
