$6\mathrm{.}55$ Computer response time is an important application of the gamma and exponential distributions. Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with a mean of $3$ seconds.

$($a$)$ What is the probability that response time exceeds $5$ seconds?

$($b$)$ What is the probability that response time exceeds $10$ seconds?

$\frac{1}{2}$ Point Bonus problems due on Moodle before Noon on October $31($Detailed solution is required$)$

HW$15$: FBD of the bucket and whole upper assembly up to EF to find force in EF and reactions at H$.$ Then draw a FBD of CDE $y$ to find force in AD $.$ AD can also be found from the FBD of the entire upper crane up to CD$.$ Draw a FBD of the bucket to find the force at K and J $.$ The shovel load acting at G is $1\mathrm{.}25$ Mg $.$ Answer: $F_{EF}=8\mathrm{.}18kN,F_{AD}=158kN$

HW$16$: Draw a FBD of ACF and EDC. Find force $P$ if the spring is compressed by $0\mathrm{.}025$ m in the position shown. $K=6k\frac{N}{m}.$

Answer: $198$N

HW$17$: Draw a FBD of AB and BC $.$ What moment is required to hold the piston in place when $=30.$ When $=0,$ the spring is unstretched. $k=15$ lb$/$in$.$

Answer: $170$ lb $-$in

HW$18$: Draw a FBD of upper handle; then FBD of the upper or lower blade to find the force on the nail. D and A are smooth contacts. AC is a smooth pin.

Answer: $F_{\text{n}\text{a}\text{i}\text{l}}=5\mathrm{.}25lb$

$\frac{1}{2}$ Point Bonus problems due on Moodle before Noon on October $31($Detailed solution is required$)$

HW$15$: FBD of the bucket and whole upper assembly up to EF to find force in EF and reactions at H$.$ Then draw a FBD of CDE $y$ to find force in AD $.$ AD can also be found from the FBD of the entire upper crane up to CD$.$ Draw a FBD of the bucket to find the force at K and J $.$ The shovel load acting at G is $1\mathrm{.}25$ Mg $.$ Answer: $F_{EF}=8\mathrm{.}18kN,F_{AD}=158kN$

HW$16$: Draw a FBD of ACF and EDC. Find force $P$ if the spring is compressed by $0\mathrm{.}025$ m in the position shown. $K=6k\frac{N}{m}.$

Answer: $198$N

HW$17$: Draw a FBD of AB and BC $.$ What moment is required to hold the piston in place when $=30.$ When $=0,$ the spring is unstretched. $k=15$ lb$/$in$.$

Answer: $170$ lb $-$in

HW$18$: Draw a FBD of upper handle; then FBD of the upper or lower blade to find the force on the nail. D and A are smooth contacts. AC is a smooth pin.

Answer: $F_{\text{n}\text{a}\text{i}\text{l}}=5\mathrm{.}25lb$