The diameters of metal rods may be assumed to have a normal distribution with mean $\mu$ cm and st

Question

The diameters of metal rods may be assumed to have a normal distribution with mean $\mu$ cm and standard deviation $\sigma$ cm. It was known that $93$% of all rods produced have diameters exceeding $0.05$ m and $6.5$% have diameters exceeding $0.052$ m, find the values of $\mu$ and $\sigma$.

Hence, find the probability that the diameter of a rod is between $4.96$ cm and $5.02$ cm.

Accepted Answer

$\mu=5.10\text{ cm}$, $\sigma=0.0669\text{ cm}$; $P(4.96<D<5.02)=0.101$

Using Standardization to Solve μ and σ

Using Standardization to Solve μ and σ

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