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 asneeded.)

b) What are the mean and standard deviation for thisdistribution?

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 asneeded.)

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 asneeded.)

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 asneeded.)

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 asneeded.)

f) What time represents the 75th percentile of thisdistribution?

(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