Respuesta :
When the weight of laboratory grasshoppers follows a normal distribution, with a mean of 90 grams and a standard deviation of 2 grams, 95% of grasshoppers weigh between 86 and 94 grams.
What is normal distribution?
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Let W be the sample of weight of laboratory grasshoppers.
W follows N(90, 2)
To calculate P(86 < W < 94)
[tex]P ( 86 < W < 94 ) \\\\P ( \frac{86 - 90}{2} < \frac{W - 90}{2} < \frac{94 - 90}{2} )\\\\P(-2 < Z < 2)\\[/tex]
= 95% (approximately)
(using excel function NORM.S.DIST(2,TRUE)-NORM.S.DIST(-2,TRUE))
Learn more about normal distribution here
https://brainly.com/question/15103234
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