Math  /  Data & Statistics

QuestionWait time at the DMV has an average of 37 minutes with a standard deviation of 8 minutes.
8. What is the z score for 20 minutes? a. 2.13 yellow b. -2.13 white c. 2.12 orange d. -2.12 grey
9. What is the z -score for 60 minutes? a. 2.88 dark green b. -2.88 blue c. 2.87 light brown d. -2.87 yellow
10. What is the probability of waiting less than 20 minutes? a. 98.34%98.34 \% purple b. 98.30%98.30 \% pink c. 1.66%1.66 \% black d. 1.70%1.70 \% red
11. What is the probability of waiting less than 60 minutes? a. 99.80%99.80 \% dark brown b. 99.79%99.79 \% orange c. 00.20%00.20 \% pink d. 00.21%00.21 \% blue
12. What is the probability of waiting between 20 and 60 minutes? a. 98.14%98.14 \% blue

Studdy Solution

STEP 1

1. The distribution of wait times at the DMV is approximately normal.
2. The mean wait time is 37 minutes.
3. The standard deviation of wait times is 8 minutes.
4. Z-scores are calculated using the formula: z=Xμσ z = \frac{X - \mu}{\sigma} , where X X is the value, μ \mu is the mean, and σ \sigma is the standard deviation.
5. Probabilities are determined using the standard normal distribution table.

STEP 2

1. Calculate the z-score for 20 minutes.
2. Calculate the z-score for 60 minutes.
3. Determine the probability of waiting less than 20 minutes.
4. Determine the probability of waiting less than 60 minutes.
5. Calculate the probability of waiting between 20 and 60 minutes.

STEP 3

Calculate the z-score for 20 minutes using the formula:
z=Xμσ=20378 z = \frac{X - \mu}{\sigma} = \frac{20 - 37}{8}
z=178=2.125 z = \frac{-17}{8} = -2.125
Round to two decimal places:
z2.13 z \approx -2.13
The correct answer is:
b. -2.13 white

STEP 4

Calculate the z-score for 60 minutes using the formula:
z=Xμσ=60378 z = \frac{X - \mu}{\sigma} = \frac{60 - 37}{8}
z=238=2.875 z = \frac{23}{8} = 2.875
Round to two decimal places:
z2.88 z \approx 2.88
The correct answer is:
a. 2.88 dark green

STEP 5

Determine the probability of waiting less than 20 minutes using the z-score of -2.13.
Using a standard normal distribution table or calculator, find the probability corresponding to z=2.13 z = -2.13 .
P(Z<2.13)0.0166 P(Z < -2.13) \approx 0.0166
Convert to percentage:
1.66% 1.66\%
The correct answer is:
c. 1.66%1.66 \% black

STEP 6

Determine the probability of waiting less than 60 minutes using the z-score of 2.88.
Using a standard normal distribution table or calculator, find the probability corresponding to z=2.88 z = 2.88 .
P(Z<2.88)0.9980 P(Z < 2.88) \approx 0.9980
Convert to percentage:
99.80% 99.80\%
The correct answer is:
a. 99.80%99.80 \% dark brown

STEP 7

Calculate the probability of waiting between 20 and 60 minutes.
P(20<X<60)=P(Z<2.88)P(Z<2.13) P(20 < X < 60) = P(Z < 2.88) - P(Z < -2.13)
P(20<X<60)=0.99800.0166=0.9814 P(20 < X < 60) = 0.9980 - 0.0166 = 0.9814
Convert to percentage:
98.14% 98.14\%
The correct answer is:
a. 98.14%98.14 \% blue

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