Question

Let the random variable X follow a normal distribution with μ = 60 and σ^2=64.

a. |
Find the probability that X is greater than 70. |

b. |
Find the probability that X is greater than 45 and less than 74. |

c. |
Find the probability that X is less than 65. |

d. |
The probability is 0.2 that X is greater than what number? |

e. |
The probability is 0.05 that X is in the symmetric interval about the mean between which two numbers? |

Answer #1

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
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?

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

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 x be a continuous random variable that has a normal
distribution with μ=85 and σ=12. Assuming n/N ≤ 0.05, find the
probability that the sample mean, x¯, for a random sample of
18taken from this population will be between 81.7 and 90.4.
Round your answer to four decimal places.

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...

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