Respuesta :
Answer:
0.3594 = 35.94% probability that a truck will weigh less than 14.3 tons
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution.
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 is 15.8 tons, with a standard deviation of the sample of 4.2 tons.
This means that [tex]\mu = 15.8, \sigma = 4.2[/tex]
What is probability that a truck will weigh less than 14.3 tons?
This is the pvalue of Z when X = 14.3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14.3 - 15.8}{4.2}[/tex]
[tex]Z = -0.36[/tex]
[tex]Z = -0.36[/tex] has a pvalue of 0.3594
0.3594 = 35.94% probability that a truck will weigh less than 14.3 tons
