The average of 8 numbers is 10. the average of 6 of the numbers is 12 what is the average of the other 2 numbers
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Answer:
Probability that the sample average time taken is less than 11 minutes for Day 1 is 0.86864.
Probability that the sample average time taken is less than 11 minutes for Day 2 is 0.88877.
Step-by-step explanation:
We are given that the time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes.
Also, five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2.
(a) Let = <u>sample average time taken</u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean time = 10 minutes
= standard deviation = 2 minutes
n = sample of individuals fill out form on Day 1 = 5
Now, the probability that the sample average time taken is less than 11 minutes for Day 1 is given by = P( < 11 minutes)
P( < 11 minutes) = P(
<
) = P(Z < 1.12) = <u>0.86864</u>
<em />
<em>The above probability is calculated by looking at the value of x = 1.12 in the z table which has an area of 0.86864.</em>
(b) Let = <u>sample average time taken</u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean time = 10 minutes
= standard deviation = 2 minutes
n = sample of individuals fill out form on Day 2 = 6
Now, the probability that the sample average time taken is less than 11 minutes for Day 2 is given by = P( < 11 minutes)
P( < 11 minutes) = P(
<
) = P(Z < 1.22) = <u>0.88877</u>
<em>The above probability is calculated by looking at the value of x = 1.22 in the z table which has an area of 0.88877.</em>