Five whole numbers are written in order
1 answer:
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Answer:
The correct answer is the last option.
Step-by-step explanation:
When you have a fraction with complex numbers, the first step to simplify is to multiply up and down the conjugate of the denominator, this will eliminate the complex part of the denominator, and in this way you can separate the expression in its real and complex part.
For the expression:
The denominator conjugate is 4 + 2i
When multiplied, the denominator is:
Answer:
The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, 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.
Mean $39725 and standard deviation $7320.
This means that
Sample of 125
This means that
The probability that the sample mean would be at least $39000 is about?
This is 1 subtracted by the pvalue of Z when X = 39000. So
By the Central Limit Theorem
has a pvalue of 0.1335
1 - 0.1335 = 0.8665
The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.