Q1-a
A construction company sells 7 concrete carriers per hour. If a change in the
administration staff happened and a new staff took over . The next days after the
change took place the sales dropped to 3 carriers per hour. Is this a significant
decrease due to the changes done?
The sales rate is a poison distributed X~𝑃𝑜𝑖𝑠(λ) , λ=7 .
Then we have to test the
Null hypothesis H° : λ =7
Against the alternative explicit hypothesis H1 :λ ≤7 .
The significance probability P(X≤ 3) =∑3𝑘=0(𝜆𝑘 . exp⁡(−𝜆)/𝑘!
,k=0,1,2,3)
. ,λ=7
b- for 2 carriers per hour , the P (X≤ 2) =<5% then we reject the H° ,and thus the
decrease is significant ,which means that the change is negative.
Q2- in al -maraei company, a milk filling machine ,the number of defective bottles
is 100 bottle per day. After a maintenance program, the number of defective
bottles decreased to 60 bottles per day. Is this a significant decreese?
X : the number of defective bottles is poison distributed , X~Pois(λ) , λ=100 which
is higher than 9, so we approximate to the normal distribution.
We have to test the null hypothesis H0: λ=100 , against the alternative H1: λ <100
We have to find the P(X≤60)= , P(X≤k)=Φ{{k+0.5-λ}/√λ} ,k=60 ,λ =100 =0.0000%,
which is less than 5% , thus we reject H0 . and the decrease is
significant..
Q3- a store contains 150 tool . 55 of them are defective .if a sample of 9
tools are picked up. what is the probability that the number of
defective tools in the 9 picked ones is less or equal 4?what is the
probability to have at least 4 defective tools in the 9 picked ones?
Q4- the number of road accidents on the roads of hail is 8 per day .the ministry of transportation
responded to this occasion by improving the roads and fixing guiding plates on all the dangerous points
all over the emirate roads. The month after this program had started the accidents decreased to 3
accidents daily. Was that program effective?.
Q5-the number of Ibola virus infections in Liberia is 6 per month .the ministry of heath did not gave the
necessary attention to the event. Because of chaos and lack of attention to the health status of the
people the number of infected people increased to 10 . were the chaos and lack of attention effective in
increasing the infections? *******************
Q6-A researcher carrying up experiments in the laboratory succeeds in 45% of his experiments .what is
the probability for this researcher to fail 9 times before he succeeds 4 times?(0.041)
Q7-Hail civil defense receives 6 emergency call a day. what is the probability that the time T (wait
between two calls ) is 1, 2,3, 4, 6, 8, 12, 24 h?
, F(X≤0)=0
F(1h)=22%, F(2)=39%, F(3)=53%, F,,,,,,,,F(12)=95%.
Q8- for X~N(0,1) ;
Calculate 1-P(u≤1) ,2- P(u≥-2) ,3-P(u≥1.25), 4- P(- 2 ≤u≤1.75).
Q9- for the random variable X~N(50,16). What is the probability of P(X≤55),P(X≥55), P(44≤X≤60)?
. For this purpose ,we have to shift to the standard distribution ,with u =X-Xm/σ ,thus P(X≤55)=.
Φ(1.25)=-0.8944=0.1056 etc.
Q10- the temperature at the center of Hail at the beginning of June has an expected value of 37° C and
a variance of (σ2=16).what is the probability that the Temperature T exceeds 43 °C? what is P(T≤ 30)?