Respuesta :
Answer:
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 275 grams and a standard deviation of 19 grams
This means that [tex]\mu = 275, \sigma = 19[/tex]
What is the probability that it will weigh between 244 grams and 305 grams?
This is the p-value of Z when X = 305 subtracted by the p-value of Z when X = 244.
X = 305
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{305 - 275}{19}[/tex]
[tex]Z = 1.58[/tex]
[tex]Z = 1.58[/tex] has a p-value of 0.9429.
X = 244
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{244 - 275}{19}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a p-value of 0.0516
0.9429 - 0.0516 = 0.8913
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
