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As we increase the value of k in Shewhart control charts, the type I error will increase.

A small customer service call center receives an average of 12 calls per hour. Assume that calls arrive randomly and independently at a constant average rate.  What is the probability that no more than 1 call arrives in a 5-minute interval?

A continuous random variable X has pdf: f(x)=kx    for   0≤x≤1f(x)=kx \quad \text{for } 0 \le x \le 2 and f(x)=0f(x)=0 otherwise.

If the mean of a process is shifted, the out-of-control ARL of a X-bar control chart can always be reduced by increasing the sample size, no matter how small the mean-shift is.

Which of the following is a key deliverable produced during the Define phase?

A manufacturer produces components of which 10% are defective. The components are being packed in boxes of 5. A box is selected at random. What is the probability that exactly one defective component is in the box? 

It is known that the probability of producing a defective product in  in a manufacturing process. We want to design a control chart to monitor the number of defects in packs of size 100 (i.e., each pack contains 100 products). Please identify the upper control limit (UCL) of this chart assuming k=3.

A coffee shop’s espresso machine has customer usage times that follow an exponential distribution with an average time of 2 minutes. What is the probability that a randomly selected customer takes more than 3 minutes?

Please show your work to receive full credit. Input the numerical answer in each blank.  Find the inherent availability and achieved availability of a system given the following:

Para cada oración, cambia los verbos del presente al pretérito.  Nosotras vamos de compras el sábado.  Nosotras de compras el sábado. Por último, voy al supermercado.  Por último, al supermercado. Lalo es el primero en levantarse.  Lalo el primero en levantarse. ¿Vas a tu habitación?  ¿ a tu habitación? Ustedes son profesores.  Ustedes profesores.