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The function f(x) represents a normal distribution whose standard deviation and mean are 1 and 5, respectively. The value of f(x) at x = 5 is 
  • a)
    0.0
  • b)
    0.159
  • c)
    0.282
  • d)
    0.398
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The function f(x) represents a normal distribution whose standard devi...
According to z curve method,
z = x - u/6

here,in this case
x is given 5
u is mean 5
6 is standard deviation which is 1
so
putting the value ans is 0.
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Community Answer
The function f(x) represents a normal distribution whose standard devi...
Question: The function f(x) represents a normal distribution whose standard deviation and mean are 1 and 5, respectively. The value of f(x) at x = 5 is

Answer:
To find the value of f(x) at x = 5, we need to calculate the probability density function (PDF) of the normal distribution at x = 5. The PDF of a normal distribution is given by the formula:

f(x) = (1 / (σ * √(2π))) * e^(-((x - μ)^2) / (2 * σ^2))

where σ is the standard deviation and μ is the mean.

To calculate the value of f(x) at x = 5, we substitute the given values into the formula:

σ = 1
μ = 5
x = 5

Calculations:
f(x) = (1 / (1 * √(2π))) * e^(-((5 - 5)^2) / (2 * 1^2))
= (1 / (√(2π))) * e^(-0 / 2)
= (1 / (√(2π))) * e^0
= (1 / (√(2π))) * 1
= 1 / (√(2π))

To simplify the expression, we can approximate the value of π as 3.14:

f(x) ≈ 1 / (√(2 * 3.14))
≈ 1 / (√(6.28))
≈ 1 / 2.51
≈ 0.398

Answer:
Therefore, the value of f(x) at x = 5 is approximately 0.398. Hence, the correct answer is option 'D'.
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The function f(x) represents a normal distribution whose standard deviation and mean are 1 and 5, respectively. The value of f(x) at x = 5 isa)0.0b)0.159c)0.282d)0.398Correct answer is option 'D'. Can you explain this answer?
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