Respuesta :
Answer:
0% approximate probability that the total weight of their baggage will exceed the limit
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of a sample of size n, we have that the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]\sigma \sqrt{n}[/tex]
In this problem, we have that:
[tex]n = 100, \mu = 49*100 = 4900, s = 19\sqrt{100} = 190[/tex]
If 100 passengers will board a flight, what is the approximate probability that the total weight of their baggage will exceed the limit
This is 1 subtracted by the pvalue of Z when X = 6000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{6000 - 4900}{190}[/tex]
[tex]Z = 5.79[/tex]
[tex]Z = 5.79[/tex] has a pvalue of 1
1 - 1 = 0
0% approximate probability that the total weight of their baggage will exceed the limit
Answer
0%
Step-by-step explanation:
so i guess its asking what is the chance of a passenger going over the limit so i guses it would be the aproximent decimal .
so if 6000 divided by 100 is 60 the chance of them excedding the limit is 0% chance because the answer is even so it dosent have a decimal so each passenger wont exceed
