Question
The customer accounts of a certain departmental store have an average balance of Rs 120 and a standard deviation of Rs 40. Assuming that the account balances are normally distributed-
a. What proportion of the accounts is over Rs 150?
b. What proportion of accounts is between Rs 100 and Rs 150?
Answer :
Word Count : 390
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To solve this problem, we first need to convert the given account balances into standard scores (Z-scores) using the formula:
Z=X−μσZ = \frac{X - \mu}{\sigma}
Where:
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ZZ is the Z-score,
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XX is the raw score (account balance),
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μ\mu is the mean, and
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σ\sigma is the standard deviation.
Part (a): Proportion of accounts over Rs 150
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