Statistics and Probability Answers

Suppose the gene ‘A’ stands for tall and gene ‘a’ stands for short, and ‘A’ is dominant over
‘a’. Suppose the parents are of genotype aa and Aa.
i) In a family like this what is the probability of having a short child?
ii) In a family like this if there are four children, what is the probability that two children
are tall and two children are short?
iii) If you survey a large number of such families having four children, what is the average
number of tall children to be expected in a family?
iv) If you survey 256 families of this type, each having four children, how many families
are expected to have all tall children?

Suppose the gene ‘A’ stands for tall and gene ‘a’ stands for short, and ‘A’ is dominant over
‘a’. Suppose the parents are of genotype aa and Aa.
i) In a family like this what is the probability of having a short child?
ii) In a family like this if there are four children, what is the probability that two children
are tall and two children are short?
iii) If you survey a large number of such families having four children, what is the average
number of tall children to be expected in a family?
iv) If you survey 256 families of this type, each having four children, how many families
are expected to have all tall children?

In a railway yard, goods trains arrive at the rate of 60 trans per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 72 minutes, calculate the following:

i) The average number of trains in the queue.
ii) The probability that the queue size is greater than or equal to 10.

A grocery shop sell milk packets containing half a litre of milk. It makes bulk purchase of the same from the nearby city. Every time a purchase is made, it incurs a cost of Rs.50 towards transportation. The daily demand of packets is about 250. The holding cost is Rs. 0.10 for a packet per day to preserve it in a refrigerator. Determine the optimum quantity of a bulk purchase and the cycle time.

A lawyer commutes daily from his suburban home to his midtown office . on the average the trip one way takes 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
a) what is probability that a trip will take atleast 1/2 hour?
b) If the office opens at 9:00 a.m. and he leaves his house at 8:45 a.m. daily what percentage of the time is he late for work?
c) if he leaves the house at 8:35 a.m and coffee is served at the office from 8:50 a.m until 9:00 a.m. , what is the probability that he misses coffee?
d) find the length of time above which we find the slowest 15% of the trips.
e) find the probability that 2 of the next 3 trips will take atleast 1/2 hour?

A bag contains 8 white balls and 4 red balls. One ball is drawn from the bag and it is
replaced after noting its colour. In the second draw again one ball is drawn and its color is
noted. Find the probability that both the balls drawn are of different colours?

Find the probability that a nurse chosen at random is a male, given that the nurse does not dislike the schedule

A warehouse has only one loading dock manned by a three person crew. Trucks arrive at the loading dock at an average rate of 5 trucks per hour and the arrival rate is Poisson distributed. The loading of a truck takes 10 minutes on an average and can be assumed to be exponentially distributed. The operating cost of a truck is Rs.20 per hour and the members of the loading crew are paid Rs.8 each per hour. Would you like to advise the truck owner to add another crew of 3 persons?

A grocery shop sell milk packets containing half a litre of milk. It makes bulk purchase of the same from the nearby city. Every time a purchase is made, it incurs a cost of Rs.50 towards transportation. The daily demand of packets is about 250. The holding cost is Rs. 0.10 for a packet per day to preserve it in a refrigerator. Determine the optimum quantity of a bulk purchase and the cycle time.

A bank wishing to determine the average amount of time a customer must wait to be
served took a random sample of 100 customers and found that the mean waiting time
was 7.2 minutes. Assuming that the population standard deviation is known to be
15 minutes, find the 90% confidence interval estimate of the mean waiting time for
all the bank’s customers.