The base of a ladder is 2.8m placed away from a tree that is 4.5m tall. The end of the ladder touches the top of the tree. Calcu
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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 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.
In this problem, we have that:
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
has a pvalue of 0.5557
X = 31
has a pvalue of 0.1335
0.5557 - 0.1335 = 0.4222
42.22% probability that the weight is between 31 and 35 pounds
If you write 
, you'll notice this is really just a quadratic equation that can be factorized:
So you have
and
So you have
and