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Answer:
0.9495 = 94.95% probability that the combined weights of the turkeys will be more than 40 pounds.
Step-by-step explanation:
When the distribution is normal, we use 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.
If we add n occurences of a normal variable, we have that:
In this question, we have that:
Two turkeys, so:
What is the probability that the combined weights of the turkeys will be more than 40 pounds?
This is one subtracted by the pvalue of Z when X = 40. So
has a pvalue of 0.0505
1 - 0.0505 = 0.9495
0.9495 = 94.95% probability that the combined weights of the turkeys will be more than 40 pounds.