The number of students using the ATM on campus daily is normally distributed with a mean of 240 and a standard deviation of 50. Based upon a random sample of 100 days, what is the probability that the ATM usage averaged more than 247 students per day

The probability is 0.080757

Step-by-step explanation:

We start by calculating the z-score

z-score = (x-mean)/SD/ √n

In this case;

x = 247 , mean = 240, SD = 50 and n = 100

z-score = (247-240)/50/√100

z-score = 7/50/10

= 7/5 = 1.4

So the probability we want to calculate is;

P( x > 1.4)

we can use the standard normal distribution table for this

P(x > 1.4) = 0.080757

%40

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm