Mathematics, 27.03.2020 21:04, ashlynhenderson0323

The amount of time it takes Annie to make dinner is continuous and uniformly distributed between 19 minutes and 49 minutes. What is the probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner

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The probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner is 0.04.

Step-by-step explanation:

Let X = amount of times (in minutes) it takes Annie to make dinner.

The random variable X follows a continuous Uniform distribution with parameters a = 19 minutes and b = 49 minutes.

The probability density function of continuous Uniform distribution is:

$f_{X}(x)=\frac{1}{b-a};\ a$

Compute the value P (39 < X < 40 | X < 44) as follows:

P(39

$=\frac{\int\limits^{40}_{39} {\frac{1}{49-19}}\, dx}{\int\limits^{44}_{19} {\frac{1}{49-19}}\, dx}$

$=\frac{ \frac{1}{30}|x|^{40}_{39}}{\frac{1}{30}|x|^{44}_{19}}$

$=\frac{ \frac{1}{30}\times 1}{\frac{1}{30}\times 25}$

$=\frac{1}{25}$

=0.04

Thus, the probability that it takes Annie between 39 and 40 minutes given that it takes less than 44 minutes for her to make dinner is 0.04.

answered: Guest

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to $\frac{1}{60} hr\\$

then mult. both sides by 75 we get the ratio

75 mi. to $\frac{75}{60} hr\\$

simplifying we get

75 mi. to $\frac{5}{4} hr$

or 1.25 hr.

answered: Guest

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