Question

Suppose that 30% of the population carry the gene for a certain disease. We consider a random sample of 20 individuals. (a) [1 mark] What is the distribution of the number of people that carry the gene for the disease? (b) [2 marks] In the observed sample, 8 subjects carry the gene. What is the estimated sample proportion of gene carriers? (c) [2 marks] What is the exact probability that the sample proportion of gene carriers is bigger than 25%? (d) [3 marks] Consider the distribution of the sampling proportion of gene carriers. Is it appropriate to use the normal approximation for its distribution? If yes, compute the approximate probability that the proportion of gene carriers is bigger than 25%. If no, justify your answer.

Answer #1

(a)

Distribution of number of people that carry the gene for the
disease is **binomial distribution** **with
parameters**

**n=20 and p=0.30**

(b)

The sample proportion is

(c)

25% of 20 means 20 *0.25 = 5

The requried probability is

(d)

Using continuity correction factor we need to find the probability

any doubts please ask ! thank you ! please rate ! :))

One percent of all individuals in a certain population are
carriers of a particular disease. A
diagnostic test for this disease has a 93% detection rate for
carriers and a 2% false positive rate. Suppose that an individual
is tested. What is the specificity of the test? What is the
probability that an individual who tests negative does not carry
the disease?

Individuals who have a certain gene have a 0.65 probability of
contracting a certain disease. Suppose that 1,171 individuals with
the gene participate in a lifetime study. What is the standard
deviation of the number of people who eventually contract the
disease?

Question 5
Cystic fibrosis (CF) is a recessive gene disease meaning that a
child has to inherit a defective CF gene from each parent. This
means that there is a 25% chance of a child having cystic fibrosis
if both parents are CF carriers Hence the number of children with
CF (in a family whose parents are CF carriers) has a binomial
distribution with n = the number of children in the family and p=
0.25
i. In a family...

Question 5
Cystic fibrosis (CF) is a recessive gene disease meaning that a
child has to inherit a defective CF gene from each parent. This
means that there is a 25% chance of a child having cystic fibrosis
if both parents are CF carriers Hence the number of children with
CF (in a family whose parents are CF carriers) has a binomial
distribution with n = the number of children in the family and p=
0.25
i. In a family...

Suppose your friend Joanna is running for class president. The
proportion of individuals in a population of students who will vote
for Joanna on election day is 60%. You plan to conduct a poll of
size n and report X, the number of individuals in your poll who
plan to vote for Joanna. You also plan to compute ?̂=??, the
proportion of individuals in your poll who plan to vote for
Joanna.
a) Explain why X is a binomial random...

Suppose a simple random sample of size n=200 is obtained from a
population whose size is N = 20000
and whose population proportion with a specified characteristic
is p equals 0.8.
(a) Describe the sampling distribution of
Determine the mean of the sampling distribution
Determine the standard deviation of the sampling
distribution
(b) What is the probability of obtaining x= 168or more
individuals with the characteristic? That is, what is P(p greater
than or equal to 0.84?
(c) What is...

Suppose the waiting time at a certain checkout counter is
bimodal. With probability 0.95, the waiting time follows an
exponential distribution with a mean waiting time of five minutes.
With probability 0.05, the waiting time equals 30 minutes.
a) Compute the mean waiting time at the checkout counter.
b) Compute the variance of the waiting time at the checkout
counter.
c) Compute the probability that an individual customer waits
longer than 5 1/2 minutes at the checkout counter.
d) Using...

Suppose the waiting time at a certain checkout counter
is bimodal. With probability 0.95, the waiting time follows an
exponential distribution with a mean waiting time of five minutes.
With probability 0.05, the waiting time equals 30
minutes.
a) Compute the mean waiting time at the checkout
counter.
b) Compute the variance of the waiting time at the
checkout counter.
c) Compute the probability that an individual customer
waits longer than 5 1/2 minutes at the checkout counter.
d) Using...

Suppose the waiting time at a certain checkout counter is
bimodal. With probability 0.95, the waiting time follows an
exponential distribution with a mean waiting time of five minutes.
With probability 0.05, the waiting time equals 30 minutes. a)
Compute the mean waiting time at the checkout counter. b) Compute
the variance of the waiting time at the checkout counter. c)
Compute the probability that an individual customer waits longer
than 5 1/2 minutes at the checkout counter. d) Using...

Suppose a simple random sample of size nequals=75 is obtained
from a population whose size is Upper N equals N=25,000 and whose
population proportion with a specified characteristic is p equals
0.6
1. Describe the sampling distribution of p hat
2. Determine the mean of the sampling distribution
3. Determine the standard deviation of the sampling
distribution
4. What is the probability of obtaining xequals=48 or more
individuals with the characteristic? That is, what is
P(ModifyingAbove p with caretpgreater than or...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 41 minutes ago

asked 45 minutes ago

asked 47 minutes ago

asked 51 minutes ago

asked 52 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago