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The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None?
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The random variable X follows a normal distribution with name two and ...
Given Information:
To find: Value of p.
Solution:
Formula:
Where,
Calculation:
Since, Z is standard normal variable, we have:
Z = (X - μ) / σ
Z = (1.6 - μ) / σ
As per the question, X follows a normal distribution with name two. For a standard normal distribution, the proportion of values less than 0 is 0.5.
So, P(Z < 0)="" />
Substituting the value of Z in the above equation, we get:
P((1.6 - μ) / σ < 0)="" />
Solving for μ, we get:
μ > 1.6
This means that the mean of the normal distribution is greater than 1.6.
Now, we can use the standard normal distribution table to find the probability of Z being less than 0. To do so, we need to find the value of Z corresponding to μ = 1.6 and σ = 1.
Z = (X - μ) / σ
Z = (1.6 - 1) / 1
Z = 0.6
From the standard normal distribution table, we can see that the probability of Z being less than 0.6 is approximately 0.7257.
Therefore, the value of p is:
P(Z < 0.6)="" />
Hence, the answer is option (d) None as none of the given options match the calculated value of p.
- Random variable X follows normal distribution with name two and variable = 1.6.
To find: Value of p.
Solution:
- We know that the standard normal distribution has a mean of 0 and a standard deviation of 1.
- Any normal distribution can be standardized by subtracting the mean and dividing by the standard deviation.
- Let Z be a standard normal variable.
Formula:
- Z = (X - μ) / σ
Where,
- X = normal distribution variable
- μ = mean of the normal distribution
- σ = standard deviation of the normal distribution
Calculation:
- Given, variable of normal distribution X = 1.6
- Let mean of the normal distribution be μ and standard deviation be σ.
Since, Z is standard normal variable, we have:
Z = (X - μ) / σ
Z = (1.6 - μ) / σ
As per the question, X follows a normal distribution with name two. For a standard normal distribution, the proportion of values less than 0 is 0.5.
So, P(Z < 0)="" />
Substituting the value of Z in the above equation, we get:
P((1.6 - μ) / σ < 0)="" />
Solving for μ, we get:
μ > 1.6
This means that the mean of the normal distribution is greater than 1.6.
Now, we can use the standard normal distribution table to find the probability of Z being less than 0. To do so, we need to find the value of Z corresponding to μ = 1.6 and σ = 1.
Z = (X - μ) / σ
Z = (1.6 - 1) / 1
Z = 0.6
From the standard normal distribution table, we can see that the probability of Z being less than 0.6 is approximately 0.7257.
Therefore, the value of p is:
P(Z < 0.6)="" />
Hence, the answer is option (d) None as none of the given options match the calculated value of p.
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The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None?
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The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None?.
The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The random variable X follows a normal distribution with name two and variable = 1.6 then the value of p is a) 1/5 b) 4/5 c) 3/5 d) None?.
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