Answer:
a) 0.11%
b) 55.99%
c) 0.25%
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of 54.3 pounds and a standard deviation of 14.5 pounds.
This means that
1. What percentage of Americans' annual salad and cooking oil consumption is less than 10 pounds?
The proportion is the pvalue of Z when X = 10. So
has a pvalue of 0.0011
0.0011*100% = 0.11%.
2. What percentage of Americans' annual salad and cooking oil consumption is between 35 and 60?
The proportion is the value of Z when X = 60 subtracted by the pvalue of Z when X = 35.
X = 60
has a pvalue of 0.6517
X = 35
has a pvalue of 0.0918
0.6517 - 0.0918 = 0.5599
0.5599*100% = 55.99%
3. What percentage of Americans' annual salad and cooking oil consumption is more than 95 pounds?
The proportion is 1 subtracted by the pvalue of Z when X = 95.
has a pvalue of 0.9975
1 - 0.9975 = 0.0025
0.0025*100% = 0.25%