A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation of 0.07 seconds.
a. A person is selected at random from Group X. Find the probability that their reaction time is greater than 0.65 seconds. The participants in Group Y are 40 years or older. Their reaction times are normally distributed
b. The participants in Group Y are 40 years or older. Their reaction times are normally distributed with mean 0.592 seconds and standard deviation σ seconds. The probability that the reaction time of a person in Group Y is greater than 0.65 seconds is 0.396. Find the value of σ
c. In the study, 38 % of the participants are in Group X. A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.
d. Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.
For group \(X\) : the reaction time is normally distributed with \(\mu=0.489, \sigma=0.07\)
a) the probability that their reaction time is greater than \(0.65\) seconds = \(P(X>0.65)=P\left(Z>\frac{0.65-0.489}{0.07}\right)=P(Z>2.3)=1-P(Z<2.3)=\)
\(1-0.9893=0.0107\)
b) The probability that the reaction time of a person in Group \(Y\) is greater than \(0.65\) seconds is \(0.396\).
\(P(Y>0.65)=P\left(Z>\frac{0.65-0.592}{\sigma}\right)=0.396\)
$$ \begin{array}{l} P(Y>0.65)=P\left(Z>\frac{0.65-0.592}{\sigma}\right)=P(Z>0.2637)=0.396 \\ \frac{0.65-0.592}{\sigma}=0.2637 \end{array} $$
\(\frac{0.65-0.592}{0.2637}=\sigma\)
C) This is a conditional probability
Let \(B\) be the time that the reaction time is greater than \(0.65\)
\(P(X)=0.38, P(Y)=0.62\)
\(P(B \mid X)=0.0107\)
\(P(B \mid Y)=0.3960\)
the probability that the participant is in Group \(X\) :
\(P(X \mid B)=\frac{0.38 * 0.0107}{0.38 * 0.0107+0.62 * 0.3960}=0.0163\)
D) This can be solved using the binomial distribution:
Probability of success: \(p=0.0163\)
Total number of trials: \(\mathrm{n}=10\)
the probability that at least two of them are in Group X.: \(P(X \geq 2)=1-P(X \leq 1)\)
$$ \begin{array}{l} P(X \geq 2)=1-0.9890=0.0110 \\ \sigma=0.22 \end{array} $$
A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.48...
A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation of 0.07 seconds. a. A person is selected at random from Group X. Find the probability that their reaction time is greater than 0.65 seconds. The participants in Group Y are 40 years or older. Their reaction times are normally distributed b....
Nan MAT238 ormal Distribution Review 1) Suppose the reaction times of teenage drivers are normally distributed with a mean of 0.53 seconds and a standard deviation of 0.11 seconds (a) What is the probability that a teenage driver chosen at random will have a reaction time less than 0.65 seconds7 5 3 (b) What proportion of teenage drivers has a reaction time greater than 0.72 seconds?
Reaction time is normally distributed, with a mean of 0.6 sec and a standard deviation of 0.1 sec. Find the probability that an individual selected at random has the following reaction times. (Round your answers to four decimal places.) (a) greater than 0.7 sec (b) less than 0.4 sec (c) between 0.4 and 0.7 sec
Replacement times for televisions are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Find the probability that a randomly selected television will need a replacement time less than 6 years.
Reaction time studies are studies in which participants receive a stimulus and the amount of time it takes for them to react is measured. In one simple type of reaction time study, each participant holds a clicker button and stares at a screen. When the participant sees a part of the screen light up, he or she clicks the button as quickly as possible. The researcher then records how much time elapsed between when the screen lit up and when...
Reaction time studies are studies in which participants receive a stimulus and the amount of time it takes for them to react is measured. In one simple type of reaction time study, each participant holds a clicker button and stares at a screen. When the participant sees a part of the screen light up, he or she clicks the button as quickly as possible. The researcher then records how much time elapsed between when the screen lit up and when...
Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15.4 years and a standard deviation of 1.4 years. Find the probability that a randomly selected quartz time piece will have a replacement time less than 12.6 years? P(X < 12.6 years) If the company wants to provide a warranty so that only 3.2% of the quartz time pieces will be replaced before the warranty expires, what is the time...
#1-4 Exit Suppose that car wash times are normally distributed with a mean of 25 minutes and a standard deviation of 3 minutes. You will be considering a group of 9 randomly selected car wash times. Answer the following questions. D 1. Given the information above, what can we say about the sampling distribution of x-bar. It is also normally distributed, because the original poplation was normally distributed. It is normally distributed because n is bigger than 30. We do...
Solve the problem. Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years. Write your answer as a decimal rounded to 4 places.
Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 11 years and a standard deviation of 1.8 years. a) Find the probability that a randomly selected quartz time piece will have a replacement time less than 7.58 years? b) If the company wants to provide a warranty so that only 0.8% of the quartz time pieces will be replaced before the warranty expires, what is the time length of...