Question

the customers accounts of certain department store have an average balance of rs 120 and standard deviation of rs 40 assuming that the account balance are normally distributed.
what proportion of the accounts is between rs 60 and rs 90..?
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Answer 1

Step-by-step explanation:

60/90

this is the correct answer

Answer 2

Answer:

The answer is 0.1598

Step-by-step explanation:

1. If X is a random variable from a normal distribution with mean (μ) and standard deviation (σ), its Z-score may be calculated by subtracting mean from X and dividing the whole by standard deviation.

                                $Z = (X-mu)/sigma$$= (X-120)/40$

2. Given mu is 120(mean) and sigma is 40(standard deviation) and we are asked to find

$P(60 < X < 90) = P((60-120)/40 < (X-120)/40 < (90-120)/40) = P(-1.5 < Z < -0.75)$

3. Here Z is standard normal variable,

P(-1.5<Z<-0.75) = area left of -0.75 in normal curve - area left of -1.5

                         = 0.2266 - 0.0668 = 0.1598

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