Question

σ " O 2 ml Is a reasonable model for the distribution of the variable x your answers to four decimal places.) amount of red dye in the paint mixture. Use the nom al distribution model to calculate the following (b) Px<5.4)-1 (d) P(4.8 < x < 5.2)-1 () P(x> 4.5) 1 You may need to use the appropriate table in Appendix A to answer this question call for corks with dameters between 1.9 and 2.1 cm. A cork not meeting the the answer to four decimal places.) おuses the wine to deteriorate; a cork that is too large doesn't nt in the bottle.) what p MacBook Air

Answer 1

a)

The following information has been provided μ 5, σ 0.2 We need to compute Pr(X <5). The corresponding z-value needed to be computed Therefore Pr(X < 5) = Pr (Z<。0.2 0.2Prs0 0.5 The following is obtained graphically Normal Distribution: PríX<5)-0.5 2.0 1.4 1.0 0.8 0.6 0.4 0.2 0.0 4.4 4.6 4.8 5.2 5.4 5.6 6.0

b)

The following information has been provided:

μ=5, σ=0.2

We need to compute Pr(X<5.4). The corresponding z-value needed to be computed:

$Z = \frac{X - \mu}{\sigma} = \frac{ 5.4 - 5}{ 0.2} = 2$

Therefore,

$\Pr(X < 5.4) = \Pr\left(Z < \frac{ 5.4 - 5}{ 0.2}\right)= \Pr(Z <e 2) = 0.9772$

c)

The following information has been provided μ 5, σ 0.2 We need to compute Pr(X 5.4). The coresponding z-value needed to be computed =5.4-5 z 0.2 Therefore 5.4-5 0.2 ) = Pr(Z < 2) = 0.9772 The following is obtained graphically: Normal Distribution: PríX<5.4)-0.9772 2.0 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 4.4 4.6 4.8 5.0 5.2 5.4 6.0

d)

We need to compute Pr(4.8 < X 5.2). The corresponding z-values needed to be computed are 4.8 5 0.2 z, Z212-5.2 5 0.2 Therefore, we get 4.8-5 5.2-5 Pr(48 < X < 5.2) = Pr = Pr(Z-1)-Pr(Z <-1) = 0.8413-0.1587 = 0.6827 The following is obtained graphically Normal Distribution: Pr(4.8<X<5.2)=0.6827 2.0 1.4 1.0 0.8 0.6 0.4 0.2 0.0 5.0 5.2 5.4 5.8 4.4 4.6 4.8 5.6 6.0

e)

We need to compute Pr(4.5). The corresponding z-value needed to be computed is Z-1- 4.5-5 0.2 Therefore, we get that 4.5-5 Pr(X4.5) Pr Z 1 0.0062 0.9938 The following is obtained graphically Normal Distribution: Pr(X>4.5)=0.9938 2.0 1.6 1.4 1.0 0.8 0.6 0.4 0.2 0.0 4.8 5.0 5.2 4.4 4.6 5.4 6.0

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