Suppose SAT Writing scores are normally distributed with a mean of 497 and a standard deviation of 109. A university plans to award scholarships to students whose scores are in the top 2%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

721.54

Step-by-step explanation:

We have to convert the 2% given in the statement into a z-score, as follows:

P (X> x) = 2% = 0.02, P (Z> z) = 0.02

thus find z such that:

P (Z <z) = 1 - P (Z> z)

P (Z <z) = 1 - 0.02

P (Z <z) = 0.98

we look for what value of z corresponds to in the normal distribution table and it is 2.06

x = m + z * sd

m is mean and sd standard deviation, replacing:

x = 497 + 2.06 * 109

x = 721.54

721.54 would be the minimum score.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

it is true

step-by-step explanation:

all the combinations add up i used   calculator