The time X(mins) for Ayesha to prepare breakfast for her family is believed to have a uniform distribution with A=25 and B=35.
a) Determine the pdf of X and draw its density curve.
b) What is the probability that time taken by Ayesha to prepare breakfast exceeds 33 mins?
c) What is the probability that cooking or preparation time is within 2 mins of the mean time?
(Hint: Identify mean from the graph of f(x))

(c)

(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Step-by-step explanation:

The random variable X follows a Uniform (25, 35).

(a)

The probability density function of an Uniform distribution is:

Then the probability density function of the random variable X is:

(b)

Compute the value of P (X > 33) as follows:

Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c)

Compute the mean of X as follows:

Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:

Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

may i see the picture? it would a lot, xox