For a fundraiser, each donor package contains 333 food vouchers and 555 raffle tickets. Complete the double number line diagram
to show the numbers of food vouchers and raffle tickets in 111, 222, 333, and 444 donor packages. Choose 1 answer: Choose 1 answer:
1 answer:
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Answer:
The blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L is 3.64.
Step-by-step explanation:
To solve this question, we have 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 random variable X, with mean and standard deviation
, the sample means of size n can be approximated to a normal distribution with mean
and standard deviation, which is also called standard error
In this problem, we have that:
What is the blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L?
This is the value of X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
By the Central Limit Theorem
The blood potassium level L such that the probability is only 0.05 that the average of four measurements is less than L is 3.64.