Question
In: Statistics and Probability
A random sample of size 36 is taken from a population having mean 20 and variance...
A random sample of size 36 is taken from a population having mean 20 and variance 9.What is the probability that the sample meanXwill be at least 21?
Solutions
Expert Solution
Solution :
Given that,
mean = 
= 20
variance=9
standard deviation = 
= 
9=3
n=36
=
=20
=
/
n = 3 / 36 = 0.5
P( > 21) = 1 - P(
<21 )
= 1 - P[(
-
) /
< (21-20) /0.5 ]
= 1 - P(z <2 )
Using z table
= 1 - 0.9772
= 0.0228
probability= 0.0228
orchestra answered 2 years agoRelated Solutions
a simple random sample of size 36 is taken from a normal population with mean 20...
a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,mean,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths place
A random sample of size n = 55 is taken from a population with mean μ...
A random sample of size n = 55 is taken from a
population with mean μ = −10.5 and standard deviation
σ = 2. [You may find it useful to reference
the z table.]
a. Calculate the expected value and the
standard error for the sampling distribution of the sample mean.
(Negative values should be indicated by a minus sign. Round
"expected value" to 1 decimal place and "standard error" to 4
decimal places.)
b. What is the probability that...
A random sample of size 40 is taken from a population with mean µ = 240...
A random sample of size 40 is taken from a population with mean
µ = 240 and standard deviation σ = 26.
i. Describe the probability distribution of the sample mean.
ii. What are the mean and the standard deviation of the sample
mean?
iii. Calculate the probability that the sample mean is between 230
and 250.
A random sample of size 40 is taken from a population with mean µ = 240...
A random sample of size 40 is taken from a population with mean
µ = 240 and standard deviation σ = 26.
i. Describe the probability distribution of the sample mean.
ii. What are the mean and the standard deviation of the sample
mean?
iii. Calculate the probability that the sample mean is between 230
and 250.
A random sample of size n = 50 is taken from a population with mean μ...
A random sample of size n = 50 is taken from a
population with mean μ = −9.5 and standard deviation
σ = 2. [You may find it useful to reference
the z table.]
a. Calculate the expected value and the
standard error for the sampling distribution of the sample mean.
(Negative values should be indicated by a minus sign.
Round "expected value" to 1 decimal place and
"standard deviation" to 4 decimal places.)
Expected Value=
Standard Error=
b. What...
A random sample of size 18 taken from a normally distributed population revealed a sample mean...
A random sample of size 18 taken from a normally distributed
population revealed a sample mean of 100 and a sample variance of
49. The 95% confidence interval for the population mean would
equal:
a)93.56 - 103.98
b)97.65 – 107.35
c)95.52 -104.65
d)96.52 – 103.48
A simple random sample of size n=36 is obtained from a population with mean=89 and standard...
A simple random sample of size n=36 is obtained from a
population with mean=89 and standard deviation = 6
(c) What is P ( x overbar less than or equal to 86.65)?
(d) What is P(88.5 < x overbar < 91.25)?
(a) Describe the sampling distribution of x overbar.
(b) What is P ( x overbar > 90.85 )?
A random sample of size n = 225 is taken from a population with a population...
A random sample of size n = 225 is taken from a
population with a population proportion P = 0.55.
[You may find it useful to reference the z
table.]
a. Calculate the expected value and the
standard error for the sampling distribution of the sample
proportion. (Round "expected value" to 2 decimal places and
"standard error" to 4 decimal places.)
b. What is the probability that the sample
proportion is between 0.50 and 0.60? (Round “z”
value to 2...
A random sample of size n = 130 is taken from a population with a population...
A random sample of size n = 130 is taken from a
population with a population proportion p = 0.58.
(You may find it useful to reference the z
table.)
a. Calculate the expected value and the
standard error for the sampling distribution of the sample
proportion. (Round "expected value" to 2 decimal places and
"standard error" to 4 decimal places.)
b. What is the probability that the sample
proportion is between 0.50 and 0.70? (Round “z”
value to 2...
Random sample of size n=19 is taken from a Normal population, sample mean is 11.5895, standard...
Random sample of size n=19 is taken from a Normal population,
sample mean is 11.5895, standard deviation is 1.0883.
1. At the 2% level, test whether it is reasonable to believe
that the true population variance is larger than 1.
Using the scenario from above, do the following
2. Derive the power function. Show your work.
3. Using R, graph the power function for 0.5 < sigma^2 <
3.5.
4. Pretend that the sample size was actually 56. Plot this...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- You currently have $55,000 in your retirement account. You will make deposits of $11,000/year into your account...
- Using the Comparable Interface Write a class Compare3 that provides a static method largest. Method largest...
- Category Prior Year Current Year Accounts payable 3,173.00 5,942.00 Accounts receivable 6,838.00 9,022.00 Accruals 5,615.00 6,173.00...
- A. What is the Porsche's competitive strategy? In your answer, include two corporate policies that manifest...
- Represent -60 in binary using 8-bit signed magnitude. Add the following unsigned 8 bit binary numbers...
- Let A[1..n] be an array of distinct positive integers, and let t be a positive integer....
- According to Pablo Picasso, "Every act of creation is, first of all, an act of destruction."...
ADVERTISEMENT