Find each measurement indicated. Round your answers to the nearest tenth.
1 answer:
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Let 
denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by 
, each independently and identically distributed with distribution 
.
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
, then the sampling distribution 
with 
being the size of the sample.
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to
Answer:
18.67% probability that the sample proportion does not exceed 0.1
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.
For the sampling distribution of a sample proportion, we have that
In this problem, we have that:
What is the probability that the sample proportion does not exceed 0.1
This is the pvalue of Z when X = 0.1. So
has a pvalue of 0.1867
18.67% probability that the sample proportion does not exceed 0.1