The average number of miles driven on a full tank of gas in a certain model car before its​ low-fuel light comes on is 309. Assume this mileage follows the normal distribution with a standard deviation of 41 miles. Complete parts a through d below.


Q4)  For a standard normal​ distribution, determine the following probabilities.

​a)​ P(z>1.44)

​b)​ P(z>−0.53​)

​c)​ P(−1.77≤z−0.73​)

​d) P(−1.76≤z≤0.21​)

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​a) P(z>1.44​)=

​(Round to four decimal places as​ needed.) ​

b)​ P(z> −0.53​)=

​(Round to four decimal places as​ needed.)

​c)​ P(−1.77≤ z ≤−0.73​)=

​(Round to four decimal places as​ needed.) ​

d) ​ P(−1.76≤z≤0.21​)=

​(Round to four decimal places as​ needed.)

Q5)  The average number of miles driven on a full tank of gas in a certain model car before its​ low-fuel light comes on is 309. Assume this mileage follows the normal distribution with a standard deviation of 41 miles. Complete parts a through d below.

a. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel less than 340 miles on the next tank of​ gas?

​(Round to four decimal places as​ needed.)

b. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel more than 256 miles on the next tank of​ gas?

​(Round to four decimal places as​ needed.)

c. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel between 274 and 294 miles on the next tank of​ gas?

​(Round to four decimal places as​ needed.)

d. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel exactly 284 miles on the next tank of​ gas?

​(Round to four decimal places as​ needed.)

Q6) A credit score measures a​ person’s creditworthiness. Assume the average credit score for Americans is 685.Assume the scores are normally distributed with a standard deviation of 49.

​a) Determine the interval of credit scores that are one standard deviation around the mean.

​b) Determine the interval of credit scores that are two standard deviations around the mean.

​c) Determine the interval of credit scores that are three standard deviations around the mean.

​a) The interval of credit scores that are one standard deviation around the mean ranges fromnothing

tonothing.

​(Type integers or decimals. Use ascending​ order.)

​b) The interval of credit scores that are two standard deviations around the mean ranges fromto .

​(Type integers or decimals. Use ascending​ order.)

​c) The interval of credit scores that are three standard deviations around the mean ranges fromto .

​(Type integers or decimals. Use ascending​ order.)

Q7)  Assume the time required to pass through security at a particular airport follows the continuous uniform distribution with a minimum time of 8 minutes and maximum time of 34 minutes. Complete parts ​(a) through ​(f) below.

​a) Calculate the value of​ f(x).

​f(x)=

​(Type an integer or decimal rounded to three decimal places as​needed.)

​b) What are the mean and standard deviation for this​distribution?

The mean of this distribution is

​(Type an integer or a​ decimal.)

The standard deviation of this distribution is

​(Type an integer or decimal rounded to two decimal places as​needed.)

​c) What is the probability that the next passenger will require less than 27 minutes to pass through​ security?

​(Type an integer or decimal rounded to three decimal places as​needed.)

​d) What is the probability that the next passenger will require more than 21 minutes to pass through​ security?

​(Type an integer or decimal rounded to three decimal places as​needed.)​

e) What is the probability that the next passenger will require between 13 and 16 minutes to pass through​ security?

​(Type an integer or decimal rounded to three decimal places as​needed.)

​f) What time represents the 75th percentile of this​distribution?

​(Type an integer or a​ decimal.)

Q8)  For a population with a mean equal to 250

and a standard deviation equal to 35​,

calculate the standard error of the mean for the following sample sizes.

​a) 20

​b) 40

​c) 60

​a) The standard error of the mean for a sample size of 20

​(Round to two decimal places as​ needed.)

​b) The standard error of the mean for a sample size of 40

​(Round to two decimal places as​ needed.)

​c) The standard error of the mean for a sample size of 60

​(Round to two decimal places as​ needed.)

Q9) For a population with a proportion equal to 0.32​,

calculate the standard error of the proportion for the following sample sizes.

​a) 35

​b) 70

​c) 105

​a) σp=

​(Round to four decimal places as​ needed.)

​b) σp=

​(Round to four decimal places as​ needed.)

​c) σp =

​(Round to four decimal places as​ needed

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