Draw a box plot for the data: 135, 149, 156, 112, 134, 141, 154, 116, 134, 156
2 answers:
The box plot is attached.
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
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We have the mean, μ = 20 and the standard deviation, σ = 4
X ≈ N(20, 4²)
We want P(X<15)
Standardising gives
P(X<15) = P(Z<
)
P(X<15) = P(Z< -1.25) ⇒ When the value of the z-score is negative, we will read the value of z<1.25 on the z-table then subtract the answer from 1
P(X<15) = 1 - P(Z<1.25)
P(X<15) = 1 - 0.8944
P(X<15) = 0.1056
Hence, the probability that pizza takes less than 15 minutes to be delivered is 0.1056 = 10.56%
X ≈ N(20, 4²)
We want P(X<15)
Standardising gives
P(X<15) = P(Z<
P(X<15) = P(Z< -1.25) ⇒ When the value of the z-score is negative, we will read the value of z<1.25 on the z-table then subtract the answer from 1
P(X<15) = 1 - P(Z<1.25)
P(X<15) = 1 - 0.8944
P(X<15) = 0.1056
Hence, the probability that pizza takes less than 15 minutes to be delivered is 0.1056 = 10.56%