1. a normal distribution has a mean of 102 and a standard deviation of 2.9 what is the z-score of 105 round to nearest hundredth.
2. the ages of people at a concert are normally distributed with a mean of 24 years and a standard deviation of 3.2 years what is the age of a concert attendee with a z-score of -1.3 round to nearest hundredth

Question 1: z-score is 1.03

Question 2: age of a concert attendee x = 19.84

Step-by-step explanation:

Question 1

Mean = μ = 102

standard deviation = σ = 2.9

x= 105

z-score = ?

z-score = x - μ / σ

              = 105 - 102 / 2.9

              = 3 / 2.9

z-score  = 1.03

Question 2

Mean = μ = 24

standard deviation = σ = 3.2

x= ?

z-score = -1.3

z-score = x - μ / σ

- 1.3  = x - 24 / 3.2

- 1.3 * 3.2 = x -24

=>  x = -4.16 + 24

    x = 19.84

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°