A company manufactures an appliance,gives a warranty and 95 percent of its appliances do not require repair before the warranty expires.If an organization buys 10 of these appliances,calculate an interval that contains 95.44 percent of all the appliances that won't require repair.
A) $\left[ \begin{array} { l l }
8.12 & 10.88
\end{array} \right]$
B) $\left[ \begin{array} { l l }
7.43 & 11.57
\end{array} ]\right.$
C) $[ 8.81 \quad 10.19 ]$
D) $\left[ \begin{array} { l l }
8.55 & 10.45
\end{array} \right]$

Question

A company manufactures an appliance,gives a warranty and 95 percent of its appliances do not require repair before the warranty expires.If an organization buys 10 of these appliances,calculate an interval that contains 95.44 percent of all the appliances that won't require repair.
A) $\left[ \begin{array} { l l } 
8.12 & 10.88
\end{array} \right]$
B) $\left[ \begin{array} { l l } 
7.43 & 11.57
\end{array} ]\right.$
C) $[ 8.81 \quad 10.19 ]$
D) $\left[ \begin{array} { l l } 
8.55 & 10.45
\end{array} \right]$

Quizplus · Accepted Answer

The number of appliances that won't require repair follows a binomial distribution with n=10 and p=0.95. Using the normal approximation, the mean is 9.5 and the standard deviation is approximately 0.69. For 95.44% (which corresponds to approximately 2 standard deviations), the interval is [8.12, 10.88].

A Company Manufactures an Appliance,gives a Warranty and 95 Percent [8.1210.88]\left[ \begin{array} { l l } 8.12 & 10.88\end{array} \right][8.12​10.88​]

A Company Manufactures an Appliance,gives a Warranty and 95 Percent $\left[ \begin{array} { l l } 8.12 & 10.88\end{array} \right]$