The number of days each licensed driver in Marion County uses a commuter rail line annually is normally distributed with mean 66 and standard deviation 21. How many days must a driver use a commuter rail line annually to be in the top 5% of rail users? Round to the nearest integer.

31.5 days

Step-by-step explanation:

We.solve using z score formula

z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

The 5th percentile z score = -1.645

Mean = 66

Standard deviation = 21

Hence:

-1.645 = x - 66/21

-1.645 × 21 = x - 66

-34.545 = x - 66

-34.545 + 66 = x

x = 31.455 days

Approximately to the nearest round integer

= 31.5 days

Therefore, driver use a commuter rail line 31.5 days annually to be in the top 5% of rail users

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.