Statistics Solutions

[Step-by-Step] Let x be a random variable that represents the length of time it takes a student to complete Dr. Tracy Wang’s homework. From long experience,

Question: Let x be a random variable that represents the length of time it takes a student to complete Dr. Tracy Wang’s homework. From long experience, it is known that x has a normal distribution with mean \[\mu =3.6\] hours and standard deviation \[\sigma =0.5\] hour.

Convert each of the following x intervals to standard z intervals.

  1. \[x\ge 4.6\]
  2. \[x\le 4.6\]
  3. \[0\le x\le 4.6\]
  4. \[2.5\le x\le 4.5\]

(b) We proceed analogously to get

\[\left\{ x\le 4.6 \right\}=\left\{ \frac{x-3.6}{0.5}\le \frac{4.6-3.6}{0.5} \right\}=\left\{ z\le 2 \right\}\]

(c) Similarly

\[\left\{ 0\le x\le 4.6 \right\}=\left\{ \frac{0-3.6}{0.5}\le \frac{x-3.6}{0.5}\le \frac{4.6-3.6}{0.5} \right\}=\left\{ -7.2\le z\le 2 \right\}\]

(d)

\[\left\{ 2.5\le x\le 4.5 \right\}=\left\{ \frac{2.5-3.6}{0.5}\le \frac{x-3.6}{0.5}\le \frac{4.5-3.6}{0.5} \right\}=\left\{ -2.2\le z\le 1.8 \right\}\]

Find the following probabilities.

  1. \[P(x\ge 4.6)\]
  2. \[P(x\le 4.6)\]
  3. \[P(0\le x\le 4.6)\]
  4. \[P(2.5\le x\le 4.5)\]
    Price: $2.99
    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


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