Question
1.The distribution of serum levels of alpha tocopherol (serum vitamin E) is here assumed to be distributed normal with mean μ=860 μg/dL and standard deviation σ=340 μg/dL.
(a).A study is undertaken for evidence of toxicity among 2000 people who regularly take vitamin-E supplements. The investigators found that 4 people have serum alpha tocopherol levels > 2000 μg/dL. Is this an unusual number of people with toxic levels of serum alpha tocopherol?
(a).A study is undertaken for evidence of toxicity among 2000 people who regularly take vitamin-E supplements. The investigators found that 4 people have serum alpha tocopherol levels > 2000 μg/dL. Is this an unusual number of people with toxic levels of serum alpha tocopherol?
Answers
GPT 3.5
To determine if the number of people with toxic levels of serum alpha tocopherol is unusual, we need to calculate the probability of observing 4 or more people with levels > 2000 μg/dL in a sample of 2000.
First, we need to convert the values to z-scores using the formula:
z = (x - μ) / σ
For a serum level of 2000 μg/dL:
z = (2000 - 860) / 340
z = 1140 / 340
z ≈ 3.35
Next, we can calculate the probability using a standard normal distribution table or a calculator:
P(Z > 3.35) ≈ 0.0004
So, the probability of finding an individual with a serum level > 2000 μg/dL is approximately 0.0004.
To find the probability of observing 4 or more people with levels > 2000 μg/dL in a sample of 2000, we can use the binomial distribution formula:
P(X ≥ 4) = 1 - P(X ≤ 3)
Where X follows a binomial distribution with n = 2000 and p ≈ 0.0004.
Using a calculator or a computer program, we find:
P(X ≥ 4) ≈ 1 - binomcdf(2000, 0.0004, 3)
≈ 1 - 0.107
≈ 0.893
Therefore, the probability of observing 4 or more people with toxic levels of serum alpha tocopherol in a sample of 2000 is approximately 0.893.
Since this probability is relatively high (close to 1), it suggests that having 4 people with levels > 2000 μg/dL is not an unusual occurrence.
First, we need to convert the values to z-scores using the formula:
z = (x - μ) / σ
For a serum level of 2000 μg/dL:
z = (2000 - 860) / 340
z = 1140 / 340
z ≈ 3.35
Next, we can calculate the probability using a standard normal distribution table or a calculator:
P(Z > 3.35) ≈ 0.0004
So, the probability of finding an individual with a serum level > 2000 μg/dL is approximately 0.0004.
To find the probability of observing 4 or more people with levels > 2000 μg/dL in a sample of 2000, we can use the binomial distribution formula:
P(X ≥ 4) = 1 - P(X ≤ 3)
Where X follows a binomial distribution with n = 2000 and p ≈ 0.0004.
Using a calculator or a computer program, we find:
P(X ≥ 4) ≈ 1 - binomcdf(2000, 0.0004, 3)
≈ 1 - 0.107
≈ 0.893
Therefore, the probability of observing 4 or more people with toxic levels of serum alpha tocopherol in a sample of 2000 is approximately 0.893.
Since this probability is relatively high (close to 1), it suggests that having 4 people with levels > 2000 μg/dL is not an unusual occurrence.
Related Questions
The serum cholesterol levels for men in in one age group are normally distributed with mean of 178.1...
Standard Addition Question:
Serum containing Na+ gave a signal of 4.27 mV in an atomic emission...
A patient has a theophylline serum concentration of 96ng/L after taking theophylline tablet. Given t...
1.The distribution of serum levels of alpha tocopherol (serum vitamin E) is here assumed to be distr...