Question

Let the random variable X follow a normal distribution with muμequals=4040 and sigmaσ2equals=6464. a. Find the probability that X is greater than 5050. b. Find the probability that X is greater than 2020 and less than 5252. c. Find the probability that X is less than 4545. d. The probability is 0.30.3 that X is greater than what number? e. The probability is 0.070.07 that X is in the symmetric interval about the mean between which two numbers?

Answer #1

Given in the question

Mean = 40

Variance = 64, standard deviation = 8

Solution(a)

P(Xbar>50) = 1-P(Xbar<=50)

Z = (50-40)/8 = 1.25

From Z table we found p-value

P(Xbar>50) = 1- 0.8944 = 0.1056

Solution(b)

P(20<Xbar<52) = P(Xbar<52) - P(Xbar<20)

Z = (52-40)/8 = 1.5

Z = (20-40)/8 = -2.5

From Z table we found P-value

P(20<Xbar<52) = 0.9332 - 0.0062 = 0.927

Solution(c)

P(Xbar<45)

Z = (45-40)/8 = 0.625

From Z table we found P-value

P(Xbar<45) = 0.7357

Solution(d)

p-value = 0.7

Z-score = 0.525

0.525 = (Xbar-40)/8

4.2 = Xbar - 40

Xbar = 44.2

Solution(e)

Now given P-value = 0.3 and this is two tailed so P-value = 0.15
and 0.85

Z-Score = -1.04 and Z score = 1.04

-1.04 = (Xbar-40)/8

-8.32 = Xbar -40

Xbar = 31.68

1.04 = (Xbar-40)/8

8.32 = Xbar - 40

Xbar = 48.32

Let the random variable X follow a normal distribution with µ =
18 and σ = 4. The probability is 0.99 that X is in the symmetric
interval about the mean between two numbers, L and U (L is the
smaller of the two numbers and U is the larger of the two numbers).
Calculate L.

Let the random variable X follow a normal distribution
with µ = 22 and σ = 4. The probability is 0.90
that Xis in the symmetric interval about the mean between
two numbers, L and U (L is the smaller of the two numbers and U is
the larger of the two numbers). Calculate U.

5.19) Let the random variable X follow a normal distribution
with U(mu) = 50 and S2 = 64.
e. The probability is 0.05 that X is in the symmetric
interval about the mean between which two
numbers?

Let the random variable X follow a normal distribution with µ =
19 and σ2 = 8. Find the probability that X is greater than 11 and
less than 15.

Let the random variable X follow a normal distribution with µ =
18 and σ2 = 11. Find the probability that X is greater than 10 and
less than 17.

Let the random variable X follow a Normal distribution with
variance σ2 = 625.
A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is the probability that μ is between 198 and 211?
What is Z-Score1 for μ greater than 198?

For
Questions 6 - 8, let the random variable X follow a Normal
distribution with variance σ2 = 625.
Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is
the probability that population mean μ is greater than 190?
a.
What is Z-Score for μ greater than 190 ==>
b.
P[Z > Z-Score] ==>
Q7. What
is the probability that μ is between 198 and 211?
a. What
is Z-Score1 for...

1) let X be a continuous random
variable that has a normal distribution with a mean of 40 and a
standard deviation of 5. Find the probability that X
assumes a value:
a. between 32 and
35 b. between 41 and 50
c. greater than
43 d. less than 49

Let X be a random variable with a mean distribution of mean μ =
70 and variance σ2 = 15.
d) Imagine a symmetric interval around the mean (μ ± c) of the
distribution described above. Find the value of c such that the
probability is about 0.2 that X is in this interval.
Please explain how to get the answer

2. Let the random variable Z follow a standard normal
distribution, and let z1 be a possible value of Z that is
representing the 10th percentile of the standard normal
distribution. Find the value of z1. Show your
calculation.
A. 1.28
B. -1.28
C. 0.255
D. -0.255
3. Given that X is a normally distributed random variable with a
mean of 52 and a standard deviation of 2, the probability that X is
between 48 and 56 is: Show your...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 30 seconds ago

asked 39 minutes ago

asked 46 minutes ago

asked 51 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago