Question

Question 3 20 pts For the HP-162 printer cartridge, the lifetime (in pages printed) are normally distributed with a mean of 657.2 and a standard deviation of 38.4. If 17 cartridges are randomly selected, what is the probability that their mean lifetime is between 650 and 670 pages? 0.3044 O 0.2049 0.6956 0.7591 Question 4 20 pts A final exam in MTH 160 has a mean of 73.0 with standard deviation 7.8. If 45 students are randomly selected from MTH 160, find the probability that the mean of their test scores is less than 76. O 0.0049 O 0.6497 0.3503 O 0.9951

Answer 1

Solution

Question 3

Answer: 0.6956

given: = 657.2, 0 = 38.4, n=17

E- formula : 2 =

P(mean lifetime between 650 and 670) = P650 < i < 670) =?

$\Rightarrow P\left (\frac{650-657.2}{\frac{38.4}{\sqrt{17}}}<\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{670-657.2}{\frac{38.4}{\sqrt{17}}} \right )$

= P(-0.77<:<1.37)

→ P: <1.37) - P: < -0.77)

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(1.37, TRUE)" & "=NORM.S.DIST(-0.77, TRUE)" to find the probability.

→ 0.9153 -0.2197

合0.6956

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Question 4

Answer: 0.9951

given : = 73.0, o = 7.8, n = 45

E- formula : 2 =

P mean of their test score is less than 76) = PT <76) =?

$\Rightarrow P\left (\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{76-73.0}{\frac{7.8}{\sqrt{45}}} \right )$

→ P: <2.58)

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(2.58, TRUE)" to find the probability.

合0.9951