Mathematics, 14.04.2020 23:02 sog8jojo

Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min

Answers: 1

Show answers

Answers

Probability that the sample average amount of time taken on first day and second day is at most 11 min is 0.99960 and 0.99988 respectively.

Step-by-step explanation:

We are given that Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 2 min.

Also, five individuals fill out a form on one day and six on another.

Let $\bar X$ = sample average amount of time taken on each day

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = mean time taken = 8 min

$\sigma$ = standard deviation = 2 min

n = sample of individuals = 5 on first day and 6 on another day

(a) Probability that the sample average amount of time taken on first day by five individuals is at most 11 min is given by;

P( $\bar X \leq$ 11 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq \frac{11-8}{\frac{2}{\sqrt{5} } }$ ) = P(Z $\leq$ 3.35) = 0.99960

The above probability is calculated by looking at the value of x = 3.35 in the z table which gave an area of 0.99960.

(b) Probability that the sample average amount of time taken on another day by six individuals is at most 11 min is given by;

P( $\bar X \leq$ 11 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq \frac{11-8}{\frac{2}{\sqrt{6} } }$ ) = P(Z $\leq$ 3.67) = 0.99988

The above probability is calculated by looking at the value of x = 3.67 in the z table which gave an area of 0.99988.

Therefore, the probability that the sample average amount of time taken on first day and second day is at most 11 min is 0.99960 and 0.99988 respectively.

Answer from: Quest

drop out of school or go to quizlet, quizlet is better

step-by-step explanation:

Answer from: Quest

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour = $(1/1000)/(1/3600)=3600/1000=18/5=3.6 kilometer/hour$

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second= $15*3.6=54 kilometer/hour$ which is the required answer.

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Based on the graph, what is the initial value of the linear relationship? a coordinate plane is shown. a line passes through the y-axis at -2 and the x-axis at 3.

Answers: 3

Answer

Mathematics, 21.06.2019 19:30

Hi, can anyone show me how to do this problem? 100 points for this. in advance

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Louis wants to carpet the rectangular floor of his basement the basement has an area of 864 square feet the width of the basement is 2/3 its length what is the length of lewis's basement

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

Ineed the solution to this problem and the steps.

Answers: 1

Answer

You know the right answer?

Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal d...

Questions