Question

A leading magazine reported that the average number of weeks an individual is unemployed is 27 weeks. Assume that for the population of all unemployed individuals, the population mean length of unemployment is 27 weeks and the population standard deviation is 4 weeks. Find the probability that a single randomly selected value is less than 26. A) 0.1587 B) 0.8413 C) 0.3413 D) 0.5000

Answer 1

The correct answer is not among the provided options. The probability that a single randomly selected value is less than 26 weeks is approximately 0.5987.

This correct answer is none of the above.

Step-by-step explanation:

To find the probability that a single randomly selected value is less than 26, we can use the Z-score formula and the standard normal distribution. The Z-score is calculated as follows:

Z= (X−μ)/σ

where:

X is the individual data point (in this case, 26 weeks),

μ is the population mean (27 weeks),

σ is the population standard deviation (4 weeks).

Plug in these values:

Z= (26−27)/4 =−0.25

Now, we need to find the probability associated with this Z-score. Using a standard normal distribution table or calculator, we find the probability that a Z-score is less than -0.25.

Looking up -0.25 in a standard normal distribution table, the probability is approximately 0.4013.

However, since we want the probability that a value is less than 26 (not less than or equal to 26), we need to find the complement of this probability:

P(X<26)=1−P(X≥26)

P(X≥26)=0.4013, we get:

P(X<26)=1−0.4013=0.5987

So, the correct answer is not among the provided options. It seems like there might be a mistake in the options or the question. Please double-check the provided options or the question itself.

This correct answer is none of the above.