MATH SOLVE

4 months ago

Q:
# 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 costs are normally distributed, what is the probability that a family spends less than $410 per month? 0.2158 0.8750 0.0362 0.1151

Accepted Solution

A:

Are you familiar with z-scores? According to the definition,

(given numerical value) - (mean)

z = ---------------------------------------------

standard deviation

Thus, with the given numerical value equal to 410 and the std. dev. equal to 75, the corresponding z-score is

410-500 -90

z = --------------------- = --------------- = -1.2

75 75

Use a table of z-scores to determine the area under the standard normal curve to the left of z = -1.2. Your result is the probability that a given family chosen at random spends less than $410 per month.

Are you familiar with z-scores? According to the definition,

(given numerical value) - (mean)

z = ---------------------------------------------

standard deviation

Thus, with the given numerical value equal to 410 and the std. dev. equal to 75, the corresponding z-score is

410-500 -90

z = --------------------- = --------------- = -1.2

75 75

Use a table of z-scores to determine the area under the standard normal curve to the left of z = -1.2. Your result is the probability that a given family chosen at random spends less than $410 per month.