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There is a 1.70% chance that the average outstanding credit balance will exceed $623.
The z-score formula is used to solve problems with normally distributed samples.
The z score of a measure X in a set with mean μ and standard deviation σ is given by:
Z = X-μ / σ
The Z-score indicates how far the measure deviates from the mean. We examine the z-score table after determining the Z-score to determine the p-value associated with this z-score. This p-value represents the likelihood that the value of the measure is less than X or the percentile of X. Subtraction of 1 from the p-value yields the probability that the value of the measure is greater than X.
The Central Limit Theorem states that for a random variable X with mean μ and standard deviation σ, sample means of at least 30 can be approximated to a normal distribution with mean μ and standard deviation σ.
δ = σ / [tex]\sqrt{n}[/tex],
μ = 650.
σ = 420
n = 200
δ = 420 / [tex]\sqrt{200}[/tex]
δ = 29.7
Z = X-μ / σ
By the Central Limit Theorem,
Z = X-μ / δ
Z = 623 - 650/ 29.7
Z = 0.9
Z = 0.9 has a p value of 0.8830
0.9 - 0.8830 = 0.017
There is a 1.70% chance that the average outstanding credit balance will exceed $623.
To learn more about outstanding credit balance, please refer:
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