Respuesta :
Answer:
There is a 78.81% probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb.
Step-by-step explanation:
Problems of normally distributed samples can be 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]
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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 177.2 lb and a standard deviation of 35.8 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb.
Here we have that [tex]\mu = 177.2, \sigma = 35.8, X = 149[/tex]. We want to find the probality that the measure is greater than 149. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{149 - 177.2}{35.8}[/tex]
[tex]Z = -0.80[/tex]
[tex]Z = -0.80[/tex] has a pvalue of 0.2119.
So, there is a 21.19% probability that X the mean weight is lighter than 149 lb.
And a 1-0.2119 = 0.7881 = 78.81% probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb.
The probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb is 78.81%.
What is normal a distribution?
It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
We know that the formula
[tex]\rm Z = \dfrac{X -\mu}{\sigma}[/tex]
Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 177.2 lb and a standard deviation of 35.8 lb.
The probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb will be
[tex]\mu = 177.2\\\\\sigma = 35.8\\\\X = 149\\[/tex]
Then we have
[tex]\rm Z = \dfrac{X -\mu}{\sigma}\\\\Z = \dfrac{149 - 177.2}{35.8}\\\\Z = -0.80[/tex]
For Z = -0.80, the probability is 21.19%
[tex]1 - 0.2119 = 0.7881 = 78.81\%[/tex]
More about the Probability link is given below.
https://brainly.com/question/12421652
