Question

Regarding a certain normal distribution concerning the income of the individuals we are given that mean = 500 rupees and standard deviation = 100 rupees. Find the possibility that an individual selected at random will belong to the income group Rs. 420 to Rs. 570.
Select one:
a. 0.213
b. none of these
c. 0.546
d. 0.183

Answer 1

Answer:

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Answer 2

Answer:

The answer to this question is option b.

Step-by-step explanation:

To solve this problem, we will use the standard normal distribution table, also known as the Z-table.

First, we need to convert the given income range of Rs. 420 to Rs. 570 to standard units using the formula:

$Z=\frac{x-mean}{standard deviation}$

Where x is the given income range, mean is the mean income, and standard deviation is the standard deviation of the income.

For the lower bound of the income range, we have:

$Z=\frac{420-500}{100} = -0.8$

For the upper bound of the income range, we have:

$Z=\frac{570-500}{100}$

Now we can use the standard normal distribution table to find the probability of a random individual having a Z-score between -0.8 and 0.7. This probability can be calculated as the area under the standard normal curve between -0.8 and 0.7.

The probability of an individual selected at random belonging to the income group Rs. 420 to Rs. 570 is approximately 0.38 or 38%.