1 SupposeXN(12.83,4.1^2). For a value of x=28, what is the corresponding z-score? Where relevant, round your answer to three decimal places.

2. SupposeXN(13.2,3.3^2). For a value of x=9.24, what is the corresponding z-score? Where relevant, round your answer to three decimal places.

3.

Density 0.000 0.002 0.004 0.006 0.008 0.010 The above plot displays the normal probability density function for a random variable X N N(150, 402). The shaded area represents P(X g 194) = 0.864. What must P(X 2 194) be equal to? Where relevant, round your answer to three decimal places. Density 0.000 0.002 0.004 0.006 0.008 0.010 O 50 100 1 50 200 250 300 The above plot displays the normal probability density function for a random variable X m N(150, 402). The blue shaded area represents P(150 1.312 x 40 g X g 150 + 1.312 x 40) = P(97.52 g X s 202.48) = 0.81. In other words, the blue shaded area represents the probability that X is within 1.312 standard deviations ofthe mean. What must be the value of the area shaded in red? That is, what must be the value of P(X 2 202.48)? Where relevant, round your answer to three decimal places. Density 0.000 0.002 0.004 0.006 0.008 0.010 0 50 100 150 200 250 300 The above plot displays the normal probability density function for a random variable X N N(150, 402). The blue shaded area represents P(150 1.577 x 40 g X g 150 + 1.577 X 40) = P(86.92 g X 3 213.08) = 0.885. In other words, the blue shaded area represents the probability that X is within 1.577 standard deviations of the mean. What must be the combined value of both areas shaded in red? Where relevant, round your answer to three decimal places