An Internet service provider sampled 540 customers and found that 55 of them experienced an interruption in their service during the previous month. Construct a 95% confidence interval for the proportion of all customers who have experienced a service interruption. (0.080, 0.123) (0.873, 0.924) (0.076, 0.127) (0.102, 0.898)

a 95% confidence interval for the proportion of all customers who have experienced a service interruption: (0.076, 0.127).

Step-by-step explanation:

Let p be the population proportion of all customers who have experienced a service interruption.

Confidence interval for p:, where = sample proportion, n= sample size, z* = critical z-value.

Given: n = 540

z* = 1.96

The required confidence interval:

Hence, a 95% confidence interval for the proportion of all customers who have experienced a service interruption: (0.076, 0.127).

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