Respuesta :
Answer:
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:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b, a<b[/tex]
Compute the value P (39 < X < 40 | X < 44) as follows:
[tex]P(39<X<40|X<44)=\frac{P(39<X<40\ \cap \ X<44)}{P(X<44)}=\frac{P(39<X<40)}{X<44)}[/tex]
[tex]=\frac{\int\limits^{40}_{39} {\frac{1}{49-19}}\, dx}{\int\limits^{44}_{19} {\frac{1}{49-19}}\, dx}[/tex]
[tex]=\frac{ \frac{1}{30}|x|^{40}_{39}}{\frac{1}{30}|x|^{44}_{19}}[/tex]
[tex]=\frac{ \frac{1}{30}\times 1}{\frac{1}{30}\times 25}[/tex]
[tex]=\frac{1}{25}[/tex]
[tex]=0.04[/tex]
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.
