Hasil pengukuran tinggi badan 500 siswa SMA Geger berdistribusi normal dengan rata-rata 154 cm dan simpangan baku 16 cm. Jika 22,66% siswa memiliki tinggi badan lebih dari k cm, tentukan nilai k __ a. 168 b. 164 c. 166 d. 167 e. 165

Here's how to solve this problem:**1. Understand the Problem**We're dealing with a normal distribution of heights. We know the mean (μ = 154 cm) and standard deviation (σ = 16 cm). We need to find the height (k) above which 22.66% of the students fall.**2. Use the Z-score**The Z-score helps us convert a value from a normal distribution into a standard normal distribution (mean = 0, standard deviation = 1). The formula is:Z = (x - μ) / σWhere:* Z = Z-score* x = the value we're interested in (k in this case)* μ = the mean (154 cm)* σ = the standard deviation (16 cm)**3. Find the Z-score corresponding to 22.66%**Since 22.66% of students are *above* k, this means 77.34% (100% - 22.66%) are *below* k. We need to find the Z-score that corresponds to a cumulative probability of 0.7734. You can use a Z-table or a statistical calculator to find this. The Z-score corresponding to a cumulative probability of approximately 0.7734 is approximately 0.75.**4. Solve for k**Now we can plug the Z-score into the Z-score formula and solve for k:0.75 = (k - 154) / 16Multiply both sides by 16:12 = k - 154Add 154 to both sides:k = 166 cm**Therefore, the value of k is 166 cm. The correct answer is (c).**