PART 1: I am a doctor and my patient has a blood salinity of 9.28 mg/mL. I know
ID: 3306406 • Letter: P
Question
PART 1:
I am a doctor and my patient has a blood salinity of 9.28 mg/mL. I know that among healthy people that blood salinities are normally distributed with a mean of 9.00 mg/mL and a standard deviation of 0.08 mg/mL.
I want to know the probability that a randomly selected healthy person would have a blood salinity of 9.28 mg/mL or greater.
Is this a Central Limit Theorem for Means problem?
No, this is not quantitative data.
No, this is not about a sample.
No, the conditions of the Central Limit Theorem for Means are not met.
Yes, this is a Central Limit Theorem for Means problem.
PART 2:
The reaction time from seeing a light to pressing a button has a mean of 0.84 s and a standard deviation of 0.56 s. A group of 15 professional athletes are given the reaction time test and their mean reaction time is 0.60 s.
I want to know the probability that any group of 15 people could have a mean reaction time of 0.60 s or less.
Is this a Central Limit Theorem for Means problem?
No, this is not quantitative data.
No, this is not about a sample.
No, the conditions of the Central Limit Theorem for Means are not met.
Yes, this is a Central Limit Theorem for Means problem.
PART 3:
The fingernail growth rate among healthy women is normally distributed with a mean of 1.26 mm/week and a standard deviation of 0.32 mm/week. I examine a random sample of 12 women and measure the fingernail growth rate of each. The mean of this sample is 1.48 mm/week.
I want to know the probability that a sample of 12 women would have a mean fingernail growth rate of 1.48 mm/week or faster.
Is this a Central Limit Theorem for Means problem?
No, this is not quantitative data.
No, this is not about a sample mean.
No, the conditions of the Central Limit Theorem for Means are not met.
Yes, this is a Central Limit Theorem for Means problem.
PART 4:
Among healthy men, their feet are not always the same length. The difference in length of right foot minus left foot has a mean of 0 cm and a standard deviation of 0.47 cm.
I select a sample of 50 male marathon runners. I measure the feet of each and find the difference of right foot minus left foot for each. The mean difference for this sample of marathon runners is 0.11 cm.
What is the probability that a sample of 50 men would have a mean difference of 0.11 cm or greater? Express your answer as a decimal with four decimal places. If the Central Limit Theorem does not apply, give the answer -2
PLEASE MAKE SURE YOUR ANSWER IS CORRECT AND COMPLETE. THANK YOU
No, this is not quantitative data.
No, this is not about a sample.
No, the conditions of the Central Limit Theorem for Means are not met.
Yes, this is a Central Limit Theorem for Means problem.
PART 2:
The reaction time from seeing a light to pressing a button has a mean of 0.84 s and a standard deviation of 0.56 s. A group of 15 professional athletes are given the reaction time test and their mean reaction time is 0.60 s.
I want to know the probability that any group of 15 people could have a mean reaction time of 0.60 s or less.
Is this a Central Limit Theorem for Means problem?
No, this is not quantitative data.
No, this is not about a sample.
No, the conditions of the Central Limit Theorem for Means are not met.
Yes, this is a Central Limit Theorem for Means problem.
PART 3:
The fingernail growth rate among healthy women is normally distributed with a mean of 1.26 mm/week and a standard deviation of 0.32 mm/week. I examine a random sample of 12 women and measure the fingernail growth rate of each. The mean of this sample is 1.48 mm/week.
I want to know the probability that a sample of 12 women would have a mean fingernail growth rate of 1.48 mm/week or faster.
Is this a Central Limit Theorem for Means problem?
No, this is not quantitative data.
No, this is not about a sample mean.
No, the conditions of the Central Limit Theorem for Means are not met.
Yes, this is a Central Limit Theorem for Means problem.
PART 4:
Among healthy men, their feet are not always the same length. The difference in length of right foot minus left foot has a mean of 0 cm and a standard deviation of 0.47 cm.
I select a sample of 50 male marathon runners. I measure the feet of each and find the difference of right foot minus left foot for each. The mean difference for this sample of marathon runners is 0.11 cm.
What is the probability that a sample of 50 men would have a mean difference of 0.11 cm or greater? Express your answer as a decimal with four decimal places. If the Central Limit Theorem does not apply, give the answer -2
PLEASE MAKE SURE YOUR ANSWER IS CORRECT AND COMPLETE. THANK YOU
Explanation / Answer
x = blood salinity of patient
mean = 9.00 mg/ml standard deviation = 0.08 mg/ml
A patient has blood salinity 9.28 mg/ml
P( randomly selected patients blood salinity ) >= 9.28
Thus this is Central Limit theorem for means problem .
As the distribution is normally distributed and blood salinity probability can be found by Central limit theorem .
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