dyhji
04.07.2019 •
Mathematics
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
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Ответ:
0.1151
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
.
What is the probability that a family spends less than $410 per month?
This probability is the pvalue of Z when X = 410. So:
has a pvalue of 0.1151. This is the answer.
Ответ:
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.
Ответ:
If you have find the x intercept its x= -6