Suppose x is a normally distributed random variable with muμequals=1616 and sigmaσequals=22. Find each of the following probabilities. a. P(xgreater than or equals≥17.517.5) b. P(xless than or equals≤1212) c. P(16.7816.78 less than or equalsxless than or equals≤20.4620.46) d. P(11.4811.48less than or equals≤xless than or equals≤19.0619.06)

Step-by-step explanation:

Since x is a normally distributed random variable, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the random variable

µ = mean

σ = standard deviation

From the information given,

µ = 16

σ = 2

a. P(x ≥ 17.5) = 1 - (x < 17.5)

For x < 17.5

z = (17.5 - 16)/2 = 0.75

Looking at the normal distribution table, the probability corresponding to the z score is 0.77

P(x ≥ 17.5) = 1 - 0.77 = 0.23

b. P(x ≤ 12)

z = (12 - 16)/2 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

P(x ≤ 12) = 0.023

c) P(16.78 ≤ x ≤ 20.46)

For x = 16.78,

z = (16.78 - 16)/2 = 0.39

Looking at the normal distribution table, the probability corresponding to the z score is 0.65

For x = 20.46,

z = (20.46 - 16)/2 = 2.23

Looking at the normal distribution table, the probability corresponding to the z score is 0.987

Therefore,

P(16.78 ≤ x ≤ 20.46) = 0.987 - 0.65 = 0.337

d) P(11.48 ≤ x ≤ 19.06)

For x = 11.48,

z = (11.48 - 16)/2 = - 2.26

Looking at the normal distribution table, the probability corresponding to the z score is 0.012

For x = 19.06,

z = (19.06 - 16)/2 = 1.53

Looking at the normal distribution table, the probability corresponding to the z score is 0.94

Therefore,

P(11.48 ≤ x ≤ 19.06) = 0.94 - 0.012 = 0.928

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