**Say X a random variable that satisfies a normal distribution** E(X) = 15, the standard deviation is 3.
1) Write down the density function of X.

y = e^(−½(x−15)²/3²) / √[ 2π3² ]

y = e^(−(x−15)²/18) / √[ 18π ]

2) Compute P(X <= 18)

18 − 15 = 3

3 / 3 = 1

P(Z<1) = 84.13%

3) Compute P(X >= 21)

P(X>21)

21 − 15 = 6

6 / 3 = 2

P(Z>2) = 2.27%

4) Compute P(11 <= X <= 19)

P(11<X<19)

11 − 15 = −4

Z₂ = −4 / 3 = −1.333

19 − 15 = 4

Z₁ = 4 / 3 = 1.333

P(−1.333<Z<1.333) = 81.75%

Can someone verified if these are 100% correct? Thanks, you need a table for this problem though

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