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Panjang sebuah komponen yang diproduksi oleh sebuah perusahaan diperkirakan berdistribusi normal dengan rata-rata 55 cm dan simpangan baku 0.020.02 cm. Jika dipilih sebuah komponen secara acak, peluang panjang komponen terpilih kurang dari 5.045.04 cm ?

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Q. Panjang sebuah komponen yang diproduksi oleh sebuah perusahaan diperkirakan berdistribusi normal dengan rata-rata 55 cm dan simpangan baku 0.020.02 cm. Jika dipilih sebuah komponen secara acak, peluang panjang komponen terpilih kurang dari 5.045.04 cm ?
  1. Standardize Value: Step Title: Standardize the Value\newlineConcise Step Description: Convert the component length of 5.04 cm5.04\,\text{cm} to a Z-score.\newlineStep Calculation: Z=X−μσ=5.04−50.02=2Z = \frac{X - \mu}{\sigma} = \frac{5.04 - 5}{0.02} = 2\newlineStep Output: Z-score: 22
  2. Find Probability: Step Title: Find the Probability\newlineConcise Step Description: Use the Z-score to find the probability that the component length is less than 5.04 cm5.04\,\text{cm}.\newlineStep Calculation: P(X<5.04)=P(Z<2)=0.9772P(X < 5.04) = P(Z < 2) = 0.9772 (from Z-table)\newlineStep Output: Probability: 0.97720.9772

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