Question

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

Answer 1

The probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase is 0.121. This outcome is not unusual.

Step-by-step explanation:

To find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase, we need to calculate the z-score and use a z-table. The z-score formula is: z = (x - mean) / standard deviation, where x is the value we want to find the probability for, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.

Here, x = 6, mean = 8.21, and standard deviation = 1.90. Plugging in these values, we get z = (6 - 8.21) / 1.90 = -1.17.

Looking up the z-score of -1.17 in a z-table, we find that the corresponding probability is approximately 0.121. So, the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase is 0.121, or 12.1%.

Now, to determine if this outcome is unusual, we can compare it to a certain threshold. A commonly used threshold is 5% (0.05). Anything below this threshold is considered unusual. Since the probability of taking less than 6 minutes is 0.121, which is larger than 0.05, we can conclude that this outcome is not unusual.

Answer 2

Correct answer is: P(x<6) is 0.123 and it is usual.

Solution:-

Given that the time a person takes to decide which shoes to purchase follows normal distribution. Which has mean = 8.21 minutes and standard deviation 1.90

Then probability of individual takes less than 6 minutes is

P(X<6) =
`P(z<(x-mean)/(standard deviation) )`

=
`P(z<(6-8.21)/(1.90) )=P(z<-1.163)`

= 0.1230

Typically we say an event with a probability less than 5% is unusual.

But here P(X<6) = 0.123 is greater than 5% hence this is usual.