The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. A. What is the probability that a flight is more than 140 minutes?B. What is the distribution's mean? C. What is the distribution's standard deviation? D. What is the probability that a flight is less than 135 minutes?

a) 33.33%)

b) 135 minutes

c) 8.66 min

d) 50%

Step-by-step explanation:

a) the probability for a uniform distribution is

P(b<X<a) = (a-b)/(c-d) , where c and d are the maximum and minimum values

therefore the probability that the flight is more than 140 minutes ( and less than 150 since it is the maximum value)

P(140<X<150) = (a-b)/(c-d) = (150-140)/(150-120) = 10/30 = 1/3 (33.33%)

b) the mean (expected value) for a uniform probability distribution is

E(X) = (c+d)/2 = (120+150)/2 = 135 minutes

c)  the standard deviation for a uniform probability distribution is

σ²(X)= (c-d)²/12 = (150-120)²/12 = 75 min²

σ = √75 min² = 8.66 min

b) following the same procedure as in a)

P(120<X<135) = (a-b)/(c-d) = (135-120)/(150-120) = 15/30 = 1/2 (50%)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.