Answer:
95.44% of the grasshoppers weigh between 86 grams and 94 grams.
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.
Mean of 90 grams and a standard deviation of 2 grams.
This means that
What percentage of the grasshoppers weigh between 86 grams and 94 grams?
The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 86. So
X = 94
has a p-value of 0.9772.
X = 86
has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544*100% = 95.44%
95.44% of the grasshoppers weigh between 86 grams and 94 grams.