Uniform Probability Distribution 1
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A manager of a department store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 4 minutes. If it takes the elevator 30 seconds to go from floor to floor, find the probability that a hurried customer can reach the first floor in less than 2.75 minutes after pushing the elevator button on the second floor.
At First I was thinking that it is just .5 integrated over [2,4] but that was incorrect
I have unlimited submission attempts so let the answers pour out!
Thanks
probability statistics probability-distributions uniform-distribution
asked Nov 4 '14 at 23:46
user3481670user3481670
1
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add a comment |
$begingroup$
A manager of a department store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 4 minutes. If it takes the elevator 30 seconds to go from floor to floor, find the probability that a hurried customer can reach the first floor in less than 2.75 minutes after pushing the elevator button on the second floor.
At First I was thinking that it is just .5 integrated over [2,4] but that was incorrect
I have unlimited submission attempts so let the answers pour out!
Thanks
probability statistics probability-distributions uniform-distribution
asked Nov 4 '14 at 23:46
user3481670user3481670
1
$endgroup$
1
$begingroup$
Your calculation is going to have to use $2.75$ somehow.
$endgroup$
– GFauxPas
Nov 4 '14 at 23:49
add a comment |
$begingroup$
A manager of a department store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 4 minutes. If it takes the elevator 30 seconds to go from floor to floor, find the probability that a hurried customer can reach the first floor in less than 2.75 minutes after pushing the elevator button on the second floor.
At First I was thinking that it is just .5 integrated over [2,4] but that was incorrect
I have unlimited submission attempts so let the answers pour out!
Thanks
probability statistics probability-distributions uniform-distribution
asked Nov 4 '14 at 23:46
user3481670user3481670
1
$endgroup$
A manager of a department store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 4 minutes. If it takes the elevator 30 seconds to go from floor to floor, find the probability that a hurried customer can reach the first floor in less than 2.75 minutes after pushing the elevator button on the second floor.
At First I was thinking that it is just .5 integrated over [2,4] but that was incorrect
I have unlimited submission attempts so let the answers pour out!
Thanks
probability statistics probability-distributions uniform-distribution
probability statistics probability-distributions uniform-distribution
asked Nov 4 '14 at 23:46
user3481670user3481670
1
asked Nov 4 '14 at 23:46
user3481670user3481670
1
asked Nov 4 '14 at 23:46
user3481670user3481670
1
asked Nov 4 '14 at 23:46
user3481670user3481670
1
asked Nov 4 '14 at 23:46
user3481670user3481670
1
1
1
$begingroup$
Your calculation is going to have to use $2.75$ somehow.
$endgroup$
– GFauxPas
Nov 4 '14 at 23:49
add a comment |
1
$begingroup$
Your calculation is going to have to use $2.75$ somehow.
$endgroup$
– GFauxPas
Nov 4 '14 at 23:49
1
1
$begingroup$
Your calculation is going to have to use $2.75$ somehow.
$endgroup$
– GFauxPas
Nov 4 '14 at 23:49
$begingroup$
Your calculation is going to have to use $2.75$ somehow.
$endgroup$
– GFauxPas
Nov 4 '14 at 23:49
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Think about it. It takes the elevator $2$ to $4$ minutes to arrive (uniformly distributed), then another $0.5$ minutes to reach the destination. You want to know the probability of reaching the destination within $2.75$ minutes of pressing the button. So you want to know the probability that the elevator arrives before what time?
Find: $mathsf P(X leq x)$ when $Xsimmathcal{U}[2,4]$ and $x =underline{qquad}$.
Do you know the cumulative distribution function ( CDF ) of a continuous uniform distribution?
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
$endgroup$
add a comment |
$begingroup$
Hint: to arrive in less than $2.75$ minutes to the first floor, he has to wait the elevator at the second floor for a maximum of $2.25$ minutes. Which is the proportion of the area of the probability function that is identified by this value?
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
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add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Think about it. It takes the elevator $2$ to $4$ minutes to arrive (uniformly distributed), then another $0.5$ minutes to reach the destination. You want to know the probability of reaching the destination within $2.75$ minutes of pressing the button. So you want to know the probability that the elevator arrives before what time?
Find: $mathsf P(X leq x)$ when $Xsimmathcal{U}[2,4]$ and $x =underline{qquad}$.
Do you know the cumulative distribution function ( CDF ) of a continuous uniform distribution?
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
$endgroup$
add a comment |
$begingroup$
Think about it. It takes the elevator $2$ to $4$ minutes to arrive (uniformly distributed), then another $0.5$ minutes to reach the destination. You want to know the probability of reaching the destination within $2.75$ minutes of pressing the button. So you want to know the probability that the elevator arrives before what time?
Find: $mathsf P(X leq x)$ when $Xsimmathcal{U}[2,4]$ and $x =underline{qquad}$.
Do you know the cumulative distribution function ( CDF ) of a continuous uniform distribution?
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
$endgroup$
add a comment |
$begingroup$
Think about it. It takes the elevator $2$ to $4$ minutes to arrive (uniformly distributed), then another $0.5$ minutes to reach the destination. You want to know the probability of reaching the destination within $2.75$ minutes of pressing the button. So you want to know the probability that the elevator arrives before what time?
Find: $mathsf P(X leq x)$ when $Xsimmathcal{U}[2,4]$ and $x =underline{qquad}$.
Do you know the cumulative distribution function ( CDF ) of a continuous uniform distribution?
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
$endgroup$
Think about it. It takes the elevator $2$ to $4$ minutes to arrive (uniformly distributed), then another $0.5$ minutes to reach the destination. You want to know the probability of reaching the destination within $2.75$ minutes of pressing the button. So you want to know the probability that the elevator arrives before what time?
Find: $mathsf P(X leq x)$ when $Xsimmathcal{U}[2,4]$ and $x =underline{qquad}$.
Do you know the cumulative distribution function ( CDF ) of a continuous uniform distribution?
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
answered Nov 5 '14 at 0:43
Graham KempGraham Kemp
85.9k43378
85.9k43378
add a comment |
add a comment |
$begingroup$
Hint: to arrive in less than $2.75$ minutes to the first floor, he has to wait the elevator at the second floor for a maximum of $2.25$ minutes. Which is the proportion of the area of the probability function that is identified by this value?
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
$endgroup$
add a comment |
$begingroup$
Hint: to arrive in less than $2.75$ minutes to the first floor, he has to wait the elevator at the second floor for a maximum of $2.25$ minutes. Which is the proportion of the area of the probability function that is identified by this value?
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
$endgroup$
add a comment |
$begingroup$
Hint: to arrive in less than $2.75$ minutes to the first floor, he has to wait the elevator at the second floor for a maximum of $2.25$ minutes. Which is the proportion of the area of the probability function that is identified by this value?
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
$endgroup$
Hint: to arrive in less than $2.75$ minutes to the first floor, he has to wait the elevator at the second floor for a maximum of $2.25$ minutes. Which is the proportion of the area of the probability function that is identified by this value?
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
answered Nov 5 '14 at 0:43
AnatolyAnatoly
11.9k21538
11.9k21538
add a comment |
add a comment |
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1
$begingroup$
Your calculation is going to have to use $2.75$ somehow.
$endgroup$
– GFauxPas
Nov 4 '14 at 23:49