Question

Question 2 Imagine an experiment where a person is seated in front of a computer. When a certain signal flashes on the screen, the subject presses a key on the keyboard as quickly as possible. A clock measures the amount of time that elapses between the signal's appearance and the subject's keypress. This amount of time is known as the reaction time. Different subjects take different amounts of time to react to the signal. Based on research, the experimenter believes that the reaction times have a normal distribution with $\mu$ = 200 milliseconds and $\sigma$ = 25 milliseconds. 100 200 300 A) Find the percentage of subjects who have reaction times between 179 and 264 milliseconds. Use correct notation. B) Find the percentage of subjects who have reaction times that are greater than 248 milliseconds? Use correct notation. 4 C) Suppose a sample of 36 research participants is collected. Find the probability that the sample average will be less than 197. Use correct notation. D) According to the Empirical Rule for normal distributions, between what two reaction times will approximately 95% of the data lie?

          Question 2
Imagine an experiment where a person is seated in front of a computer. When a certain
signal flashes on the screen, the subject presses a key on the keyboard as quickly as
possible. A clock measures the amount of time that elapses between the signal's
appearance and the subject's keypress. This amount of time is known as the reaction
time. Different subjects take different amounts of time to react to the signal. Based on
research, the experimenter believes that the reaction times have a normal distribution
with $\mu$ = 200 milliseconds and $\sigma$ = 25 milliseconds.
100
200
300
A) Find the percentage of subjects who have reaction times between 179 and 264
milliseconds. Use correct notation.
B) Find the percentage of subjects who have reaction times that are greater than 248
milliseconds? Use correct notation.
4
C) Suppose a sample of 36 research participants is collected. Find the probability that
the sample average will be less than 197. Use correct notation.
D) According to the Empirical Rule for normal distributions, between what two
reaction times will approximately 95% of the data lie?

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Question 2
Imagine an experiment where a person is seated in front of a computer. When a certain
signal flashes on the screen, the subject presses a key on the keyboard as quickly as
possible. A clock measures the amount of time that elapses between the signal's
appearance and the subject's keypress. This amount of time is known as the reaction
time. Different subjects take different amounts of time to react to the signal. Based on
research, the experimenter believes that the reaction times have a normal distribution
with μ = 200 milliseconds and σ = 25 milliseconds.
100
200
300
A) Find the percentage of subjects who have reaction times between 179 and 264
milliseconds. Use correct notation.
B) Find the percentage of subjects who have reaction times that are greater than 248
milliseconds? Use correct notation.
4
C) Suppose a sample of 36 research participants is collected. Find the probability that
the sample average will be less than 197. Use correct notation.
D) According to the Empirical Rule for normal distributions, between what two
reaction times will approximately 95% of the data lie?

Added by Stephen D.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

09/26/2022

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Step 1: We are given that the reaction times have a normal distribution with a mean of 200 milliseconds and a standard deviation of 25 milliseconds. Show more…

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Question 2 Imagine an experiment where a person is seated in front of a computer. When a certain signal flashes on the screen, the subject presses a key on the keyboard as quickly as possible. A clock measures the amount of time that elapses between the signal's appearance and the subject's keypress. This amount of time is known as the reaction time. Different subjects take different amounts of time to react to the signal. Based on research, the experimenter believes that the reaction times have a normal distribution with µ = 200 milliseconds and σ = 25 milliseconds. 100 200 300 A) Find the percentage of subjects who have reaction times between 179 and 264 milliseconds. Use correct notation. B) Find the percentage of subjects who have reaction times that are greater than 248 milliseconds? Use correct notation. 4 C) Suppose a sample of 36 research participants is collected. Find the probability that the sample average will be less than 197. Use correct notation. D) According to the Empirical Rule for normal distributions, between what two reaction times will approximately 95% of the data lie?

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00:01 For part a of this problem, we are being asked to find what is the probability that 12, of those 12 persons have an average reaction time greater than 180.

00:14 So we first find the c scored by subtracting 180, which is the desired value, minus 190, which is the mean, divided by 20, which is the standard deviation, and this is at the same time divided by the square root of the sample size, which is the square root of 12.

00:36 Put this into our calculators, and we get that the c scored is negative 1 .7 .3 to 1 .1.

00:46 Now that we have the c score, we can find the p value, which is the probability of x being smaller than 180.

00:55 Actually not smaller it's greater than 180 and therefore this we go to our p tables using the c scores and since we're looking for a greater value every time we do greater values we have to do right -tail test and the right -tail test gives us that the p value or the probability is 0 .9584 or 95 .84 percent now we go to part b in part b, let's see, we're being as how many people are we given? we are being 12 people again.

01:35 Actually, no, we're given 16 people for this problem, and their reaction time less than 191.

01:43 So we start by looking for the c scored, 191 minus the mean of 190 divided by 20, which is the standard deviation divided by the square root of 16.

01:58 So let's put this into our calculators and we get that this c scored is equal to 0 .2.

02:05 So now that we have the c score, we can find the p value of x being smaller than 191.

02:15 And we go to our p tables, find given a c score of 0 .2...

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