10. A manufacturer knows from experience that the resistance of resistors she produces is normal with mean µ = 150Ω and the standard deviation σ = 5Ω. What percentage of the resistors will have resistance between 148 Ω and 152 Ω? Between 140 Ω and 160 Ω?

Explanation:

Using the formula for finding the Z score

Z = x-µ/σ

x is the sample size

µ is the sample mean

σ is the standard deviation

For percentage of the resistors will have resistance between 148 Ω and 152 Ω, or is calculated as shown

P(148≤x152) = Z(152-150/5) - Z(148-150/5)

P(148≤x152) = Z(0.4)-Z( - 0.4)

P(148≤x152) = 0.6554-0.3446

The Z values are from the normal distribution table.

P(148≤x152) = 0.3108

The percentage of resistor that will have between 148 and 152 ohms is 0.3108×100% = 31.08%

Similarly for resistances between 140 Ω and 160 Ω

P(140≤x160) = Z(160-150/5) - Z(140-150/5)

P(140≤x160) = Z(2.0)-Z( - 2.0)

P(140≤x160) = 0.9775-0.02275

The Z values are from the normal distribution table.

P(140≤x160) = 0.9547

The percentage of resistor that will have between 140 and 160ohms is 0.9547×100% = 95.47%

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explanation:

measure their densities same density, same sub