Respuesta :
Answer:
a) What is the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through?
0.10235
b) What proportion of cars spend between 2 and 3 minutes in the restaurant's drive-through?
= 30.917% to 90.289%
= 0.30917 to 0.90289
= 0.30917 : 090289
Step-by-step explanation:
We solve for this questions using z score formula
z-score is z = (x-μ)/σ,
where
x is the raw score,
μ is the population mean
σ is the population standard deviation.
a) What is the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through?
x = 179 seconds μ =136.64 seconds, σ = 33.4 seconds
z = (x - μ)/σ
= (179 - 136.64)/33.4
= 1.26826
Determining the probability value from Z-Table:
P(x≤ 179) = 0.89765
P(x< 179) = P(z = 1.26826) = 0.89765
P(x>179) = 1 - P(x<179)
= 1 - 0.89765
= 0.10235
Therefore, the probability that a randomly selected car will spend more than 179 seconds in the restaurant's drive-through is 0.10235
b) What proportion of cars spend between 2 and 3 minutes in the restaurant's drive-through?
Converting the time in minutes to seconds
1 minute = 60 seconds
2 minutes = 60 seconds × 2
= 120 seconds
3 minutes = 60 seconds × 3
= 180 seconds
For 2 minutes = 120 seconds
x = 120 seconds μ =136.64 seconds, σ = 33.4 seconds
Since we are asked to find proportion, n =
z = (x - μ)/σ
= (120 - 136.64)/33.4
= -0.4982
Determining the probability value from Z-Table:
P(x≤ 120) = 0.30917
P(x = 120) = P(z = -0.4982) = 0.30917
Converting to percentage
0.30917 × 100 = 30.917 %
This means 30.917% spend 2 minutes in the restaurant drive through
For 3 minutes
x = 180 seconds μ =136.64 seconds, σ = 33.4 seconds
z = (x - μ)/σ
= (180 - 136.64)/33.4
=1.2982
Determining the probability value from Z-Table:
P(x≤ 180) = 1.2982
P(x = 180) = P(z =1.2982) = 0.90289
Converting to percentage
0.90.289 × 100 = 90.289%
This means 90.289% spend 3 minutes in the restaurant drive through
The proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is:
= 30.917% to 90.289%
= 0.30917 to 0.90289
= 0.30917 : 090289
