In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume
1 answer:
Answer:
The approximate probability that the total weight of the passengers exceeds 4432 pounds is 0.2709
Step-by-step explanation:
No. of passengers = n = 21
We are supposed to find the approximate probability that the total weight of the passengers exceeds 4432 pounds
Z=0.612
refer z table
P(Z<211)=0.7291
P(Z>211)=P(Z>4432)=1-0.7291=0.2709
Hence the approximate probability that the total weight of the passengers exceeds 4432 pounds is 0.2709
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Answer:
3.67% probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.
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 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
Find the probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.
This is the pvalue of Z when X = 0.809.
By the Central Limit Theorem
has a pvalue of 0.0367
3.67% probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.