Question

r classes. If 8 adult smartphone users are randomly selected, find the probability that at least 5 of them use their smartphones in meetings or classes. The probability is (Round to four decimal places as needed.)

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between

47.0 and 52.0

minutes. Find the probability that a given class period runs between

50.75 and 51.5 minutes.

Find the probability of selecting a class that runs between 50.75 and 51.5 minutes.

Answer 1

#1.
Here, n = 8, p = 0.49, (1 - p) = 0.51 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 5).
P(X >= 5) = (8C5 * 0.49^5 * 0.51^3) + (8C6 * 0.49^6 * 0.51^2) + (8C7 * 0.49^7 * 0.51^1) + (8C8 * 0.49^8 * 0.51^0)
P(X >= 5) = 0.2098 + 0.1008 + 0.0277 + 0.0033
P(X >= 5) = 0.3416

#2.
Here, the given values of lower limit, a = 47 and upper limit, b = 52

For Uniform Distribution,
P(x1 <= X <= x2) = (x2 - x1)/(b - a)
P(50.75 <= X <= 51.5) = (51.5 - 50.75)/(52 - 47)
P(50.75 <= X <= 51.5) = 0.1500