The distribution is best described as: \( \square \) Uniform The correct notation for this density curve is: \( \square \) \( U(16,24) \) Compute the following probabilities. State answers as decimals. \[ \begin{array}{l} P(X \leq 18)=\text { type your answer... } \\ P(X>19)=\text { type your answer... } \end{array} \] Calculate the following: \[ Q_{1}=18 \] BMedian = \( \square \) 20 \[ Q_{3}= \] \[ \mathrm{IQR}= \] \( \square \) \( \square \) \[ \mu= \] \( \square \) \[ \sigma= \] \( \square \)

We are given a Uniform distribution on the interval [16, 24], which we denote as U(16, 24). 1. Probabilities  a. P(X ≤ 18)   For a uniform distribution, the probability is proportional to the length. Thus:    P(X ≤ 18) = (18 – 16) / (24 – 16) = 2/8 = 0.25  b. P(X > 19)   Here, compute the length from 19 to 24:    P(X > 19) = (24 – 19) / (24 – 16) = 5/8 = 0.625 2. Quantiles and Related Measures  a. Q1 is given as 18.  b. The median (50th percentile) is computed by:    Median = (16 + 24) / 2 = 40/2 = 20  c. Q3 is the 75th percentile:    Q3 = 16 + 0.75*(24 – 16) = 16 + 0.75*8 = 16 + 6 = 22  d. IQR (Interquartile Range) = Q3 – Q1 = 22 – 18 = 4 3. Mean and Standard Deviation  a. The mean (μ) for a uniform distribution is:    μ = (16 + 24) / 2 = 20  b. The standard deviation (σ) is given by:    σ = (b – a) / √12 = 8 / √12 = 8 / (2√3) = 4 / √3    Approximating √3 ≈ 1.732, we have:    σ ≈ 4 / 1.732 ≈ 2.31 Summary of answers: • Distribution: Uniform • Correct notation: U(16, 24) • P(X ≤ 18) = 0.25 • P(X > 19) = 0.625 • Q1 = 18 • Median = 20 • Q3 = 22 • IQR = 4 • μ = 20 • σ ≈ 2.31