Respuesta :
Answer:
42.22% probability that the weight is between 31 and 35 pounds
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 34.6, \sigma = 2.8[/tex]
What is the probability that the weight is between 31 and 35 pounds
This is the pvalue of Z when X = 35 subtracted by the pvalue of Z when X = 31. So
X = 35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 34.6}{2.8}[/tex]
[tex]Z = 0.14[/tex]
[tex]Z = 0.14[/tex] has a pvalue of 0.5557
X = 31
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 34.6}{2.8}[/tex]
[tex]Z = -1.11[/tex]
[tex]Z = -1.11[/tex] has a pvalue of 0.1335
0.5557 - 0.1335 = 0.4222
42.22% probability that the weight is between 31 and 35 pounds
