(a)What percent of the scores are less than 19? (b) out of 1500 randomly selected scores, about how many would be expected to be greater than 21

(a) 45.4%

(b) 591

Step-by-step explanation:

(a) μ = 19.6, σ = 5.2

First, find the z-score.

z = (x − μ) / σ

z = (19 − 19.6) / 5.2

z = -0.115

Use a chart or calculator to find the probability.

P(Z < -0.115) = 0.454

45.4% of the scores are less than 19.

(b) First, find the z-score.

z = (x − μ) / σ

z = (21 − 19.6) / 5.2

z = 0.269

Use a chart or calculator to find the probability.

P(Z > 0.269) = 1 − P(Z < 0.269)

P(Z > 0.269) = 1 − 0.606

P(Z > 0.269) = 0.394

39.4% of the scores are greater than 21.  There are 1500 scores, so 39.4% of that is 591.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.