Posted: May 1st, 2022

The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.2 minutes

The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.2 minutes. 48 runners are randomly chosen to run the 5K fun run. Spherical all solutions to four decimal locations the place attainable and assume a traditional distribution.

a. What is the distribution of XX? XX ~ N(,)

b. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)

c. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)

d. If one randomly chosen runner is timed, discover the chance that this runner’s time will likely be between 24.1237 and 24.5237 minutes.

e. For the 48 runners, discover the chance that their average time is between 24.1237 and 24.5237 minutes.

2.

Every sweat store employee at a pc manufacturing facility can put collectively 5 computer systems per hour on average with a standard deviation of zero.eight computer systems. 50 staff are randomly chosen to work the subsequent shift at the manufacturing facility. Spherical all solutions to four decimal locations the place attainable and assume a traditional distribution.

a. What is the distribution of XX? XX ~ N(,)

b. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)

c. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)

d. If one randomly chosen employee is noticed, discover the chance that this employee will put collectively between four.9 and 5 computer systems per hour.

e. For the 50 staff, discover the chance that their average variety of computer systems put collectively per hour is between four.9 and 5.

f. Discover the chance 50 individual shift will put collectively between 240 and 245 computer systems per hour.

g. For half e) and f), is the assumption of regular crucial? YesNo

h. A sticker that claims “Nice Dedication” will likely be given to the teams of 50 staff who’ve the high 10% productiveness. What is the least whole variety of computer systems produced by a bunch that receives a sticker? computer systems per hour (spherical to the nearest pc)

i. Discover the chance that the randomly chosen 48 individual workforce may have a complete time greater than 1132.eight.

j. For half e) and f), is the assumption of regular crucial? NoYes

ok. The high 15% of all 48 individual workforce relay races will compete in the championship spherical. These are the 15% lowest instances. What is the longest whole time relay workforce can have and nonetheless make it to the championship spherical? minutes.

three. Suppose that the quantity of time that college students spend learning in the library in a single sitting is usually distributed with imply 46 minutes and standard deviation 21 minutes. A researcher noticed 6 college students who entered the library to research. Spherical all solutions to four decimal locations the place attainable.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly chosen pupil is timed, discover the chance that this pupil’s time will likely be between 33 and 40 minutes.
For the 6 college students, discover the chance that their average time learning is between 33 and 40 minutes.
Discover the chance that the randomly chosen 6 college students may have a complete research time greater than 324 minutes.
For half e) and f), is the assumption of regular crucial? NoYes
The high 10% of the whole research time for teams of 6 college students will likely be given a sticker that claims “Nice dedication”. What is the least whole time group can research and nonetheless obtain a sticker? minutes
four.

The average sum of money that folks spend at Don Mcalds quick meals place is $7.1300 with a standard deviation of $1.7300. 11 clients are randomly chosen. Please reply the following questions, and spherical all solutions to four decimal locations the place attainable and assume a traditional distribution.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
What is the chance that one randomly chosen buyer will spend greater than $6.3976?
For the 11 clients, discover the chance that their average spent is greater than $6.3976.
Discover the chance that the randomly chosen 11 clients will spend lower than $70.3736.
For half e) and f), is the assumption of regular crucial? YesNo
The proprietor of Don Mcalds offers a coupon for a free sundae to the three% of all teams of 11 individuals who spend the most cash. No less than how a lot should a bunch of 11 spend in whole to get the free sundae? $
5.

The average rating for video games performed in the NFL is 20.7 and the standard deviation is 9.2 factors. 42 video games are randomly chosen. Spherical all solutions to four decimal locations the place attainable and assume a traditional distribution.

What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
P(¯xx¯ < 20.3706) =
Discover the 68th percentile for the imply rating for this pattern measurement.
P(20.6706 < ¯xx¯ < 22.4098) =
Q3 for the ¯xx¯ distribution =
P(∑x∑x < 914.3652) =
For half c) and e), is the assumption of regular crucial? Sure or No

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The 5K fun run takes an average of 24 minutes to full, with a standard deviation of 2.2 minutes. A complete of 48 runners are chosen at random to take part in the 5K fun run. If attainable, spherical all solutions to 4 decimal locations and assume a traditional distribution.

a. What is XX’s chance distribution? XX N (,)

b. What is the chance distribution of xx? xx N (,)

c. What is the xx distribution? N xx xx xx xx xx xx xx (,)

d. Decide the chance that one randomly chosen runner’s time will fall between 24.1237 and 24.5237 minutes.

e. Calculate the chance that the 48 runners’ average time is between 24.1237 and 24.5237 minutes.

2.

In a pc manufacturing facility, every sweatshop employee can assemble 5 computer systems.

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