Question

the amount of sleep per night of us.adults follows a normal distribution with mean 7.5 hours and A lot of research is conducted on the sleeping habits of US adults. One study reported that standard de 12 hours Question 1 1 The shaded area in the image below represents which of the follow n PXX-5 PSX9.5) PEX- S X 9.5) PX X5

Answer 1

Solution

$\mathbf{given:}\;\mu=7.5,\;\sigma=1.2$

${\color{Blue} \mathbf{Question\;13\;of\;18}}$

${\color{Red} \mathbf{P(8.5<X\leq 9.5)}}$

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Question 14 of 18

Use empirical rule

99.79 95% 689 0.15% 0.15%b 2.35% 13.5% 34% 34% 13.5%; 2.3596 30 - | 20 - ه1 - ع ع1 + 2 + 30 +

Plugin given values

99.7% 95% 68% 0.15% | 0.15% 2.35%:13.5%; 34% 134% 13.5% 2.35% | 3.9 5.116.3 7.5 | 8.7 19.9 |11.1]

$P(more\;than\;8.7)\Rightarrow P(X>8.7)=?$

$P(X>8.7)=13.5\%+2.35\%+0.15\%$

$P(X>8.7)=16{\color{Red} }\%$

$P(X>8.7)\approx {\color{Red} \mathbf{0.16}}$

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${\color{Blue} \mathbf{Question\;15\;of\;18}}$

9.7% 195% 68% 0.15% | 0.15% 2.35% 13.5%; 34% 34%:13.5%; 2.35% | 3.9 15.1 | 6.3 7.5 | 8.7 | 9.9 |11.1

$\mathbf{Lowest\;2.5\%}=\mathbf{{\color{Red} 5.1}}$