For a normal distribution, mean = median = mode, so

Lower Quartile: P(Z<z) = 0.25

so z = -0.67449, (using tables or calculator)

-0.67449 = (x - 30)/8, so x = Q1 = 24.6041

Upper Quartile: P(Z<z) = 0.75

so z = 0.67449

0.67449 = (x - 30)/8, so x = Q3 = 35.3959

Q1 and Q3 are equidistant from the Median

The area under the standard normal curve corresponding to Q1 = 0.2500 and Q3 = 0.7500

The corresponding z values are for Q1 = - 0.675 and for Q3 = + 0.675

Median = 30 and standard deviation = 8

- 0.675 = (X - 30)/8

- 5.4 = X - 30

X = 30 - 5.4 = 24.6

Lower quartile = Q1 = 24.6

+ 0.675 = (X - 30)/8

+ 5.4 = X - 30

X = 30+5.4 = 35.4

Upper quartile = Q3 = 35.4

ok so first shall we see what we've, usual deviation is two.6 propose is unknown P(Z<7) = .25 The formulation we can use is z= propose-x/usual deviation to locate z we pass to table a and locate the p-fee of .25 that's at z=-.674 (or do basically invNorm(.25) on your calculator. next our parameter is whilst Z<7 so 7 Now shall we plug in what we've: -.674 = (propose-7)/2.6 next remedy for the propose, the formulation looks like this: (-.674*2.6) + 7 =propose the respond is 5.2476