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## Question 1 of 6

A company has outsourced the manufacturing of a gasket for one of their valves to a company in China. The gaskets are received in very large lots (with many thousands of gaskets). The company controls a batch by sampling 200 gaskets at random from the lot, these are classified as defective or intact. A lot is accepted if there are at most 2 defective item among the controlled ones.

What is the approximate probability of accepting a lot if the percentage of defectives is $0.4\%$?

## Question 2 of 6

In a redesigned valve the socalled “elasticity modulus’’ of the material is important for the functionality. To compare the elasticity modulus of 3 different brass alloys, samples from each alloy was purchased from 5 different manufacturers. The measurements in the table below indicates the measured elasticity modulus in GPa:

Brass alloy   Row sum
M1 M2 M3
Manufacturer A 82.5 90.9 75.6 249.0
Manufacturer B 83.7 99.2 78.1 261.0
Manufacturer C 80.9 101.4 87.3 269.6
Manufacturer D 95.2 104.2 92.2 291.6
Manufacturer E 80.8 104.1 83.8 268.7
Column sum 423.1 499.8 417.0

Consider only the data for brass alloy M1. The median and the upper quartile for these become: (using the eBook Chapter 1 definition) end:text

## Question 3 of 6

The arrival of guests wishing to check into a hotel is assumed in the period between 14 (2pm) and 18 (6 pm) o’clock to be described by a poisson proces (arrivals are assumed evenly distributed over time and independent of each other). From extensive previous measurements it has been found that the probability that no guests arrive in a period of 15 minutes is 0.30. ($P (X_{15min} = 0) = 0.30$, where $X_{15min}$ describes the number of arrivals per 15 min).

The expected number of arrivals per 15 min, and the probability that in a period of 1 hour 8 guests or more arrive are:

## Question 4 of 6

On a shelf 9 apparently identical ring binders are postioned. It is known that 2 of the ring binders contain statistics exercises, 3 of the ring binders contain math problems and 4 of ring binders contain reports. Three ring binders are sampled without replacement.

The random variable X describes the number of ring binders with statistics exercises among the 3 chosen ones.The mean and variance for the random variable X is:

## Question 5 of 6

If you did the previous exercise, the following is a repetition: On a shelf 9 apparently identical ring binders are postioned. It is known that 2 of the ring binders contain statistics exercises, 3 of the ring binders contain math problems and 4 of ring binders contain reports. Three ring binders are sampled without replacement.

The probability (${P_1}$) that all the three chosen ring binders contain reports and the probability (${P_2}$) to chose exactly one of each kind of ring binder are:

## Question 6 of 6

A PC user noted that the probability of no spam emails during a given day is 5\%. ($P (X = 0) = 0.05$, where $X$ denotes the number of spam emails per day). The number of spam emails per day is assumed to follow a poisson distribution.

The expected number of spam emails per day and the probability of getting more than 5 spam mails on any given day are: