HOMEWORK (SESSION 6)
S6.1
The score of English tests for students at a high school is normally distributed with a mean of 462
and a standard deviation of 23.
a. What percentage of all students is between 435 and 485 scores?
b. What percentage of all students has scores higher than 500?
c. What percentage of all students has scores lower than 380?
d. What percentage of all students has scores lower than 510?
S6.2
In a Vissan farm, when the ducks are 12 weeks old, they are processed. Their weights are
distributed normally, with a mean of 3.8 kilogram(kg) and a standard deviation of 0.6 kg.
According to their weight, the farm has divided these ducks into three categories: little (less than
3.5 kg), medium (between 3.5 kg and 4.9 kg), and large (more than 4.9 kg)
a. What percentage of these ducks will fall into each category?
b. Determine the distribution of weight's 60th percentile. Find c, in other words, such that P(X
<a) = 0.60.
c. Suppose that 6 ducks are selected at random. What is the probability that 4 of them will
be little?
d. Ducks are measured accurately and any which are little or large are rejected. Out of a batch
of 4,000 ducks, how many would be rejected?
S6.3
A commercial bank's branch observes that the customer deposit growth over one day is normally
distributed, with a mean of 1.5 billion VND and a standard deviation of 9.7 billion VND. A
negative increase, often known as a loss, shows that the withdrawal exceeded the deposit.
a. Determine X at which there is a 5% chance that the balance sheet will lose more than
x billion in a given day.
b. For the X you found in part (a), what is the probability that the balance sheet will
increase in value by more than X VND in one day?
S6.4
The lifetime of a light is ๐ hours, where ๐ can be modelled by an exponential distribution with
parameter ๐ = 0.0125.
a. Find the mean and variance of the lifetime of a light.
b. Find the probability that the lifetime of a light is less than 100 hours;
c. Find the probability that the lifetime of a light is between 50 hours and 150 hours.
d. What is the minimum hour if the probability of a light is less than 20%?
e. Determine the median lifetime of a light. Combining with the results in (a), comment on
the shape of distribution.
f. Find the IQR (Interquartile Range) of the lifetime of the light.
S6.5
