1.) For the following normal distribution, give the x-values of the inflection p

Question

1.) For the following normal distribution, give the x-values of the inflection points of the curve (the points where the curve's concavity changes).

x ~ N(0, 5)

2) For the following normal distribution, give the x-values of the inflection points of the curve (the points where the curve's concavity changes).

x ~ N(-5, 1.25)

3) Which of the following t distributions is closest to the standard normal distribution?

a) t distribution with 4 df

b) t distirbution with 5 df

c) t distirbution with n = 4

d) t distirbution with n = 5

4) Identify the value on the horizontal axis that corresponds to the highest point on the density curve of a chi-square distribution with 16 degrees of freedom.

5.) Find P(x > 2.75), where x ~ N(2, 1.25).

Thank you in advance!!

Explanation / Answer

1)

Its density has two inflection points (where the second derivative of f is zero and changes sign), located one standard deviation away from the mean, namely at x = and x = + .

=0 , . = 5

hence x = 0 - 5 = -5

x = 0 + 5 = 5

2)

= -5 , . = 1.25

hence x = -5 -1.25 = -6.25

x = -5+ 1.25 = -3.75

3) more is the df ,more close it is to normal

df = n-1 , hence

b) t distirbution with 5 df is is closest to the standard normal distribution

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