Question

Given a normal distribution with Mean of 100 and Standard deviation of 10, what is the probability that

between what two X values (symmetrically distributed around the mean) are 80% of the values?

Answer #1

Mean= 100

Std= 10

Data will be distributed equally on both sides of the mean. mean= 0.5

So, the probability is divided by 2 = 0.8/2 =0.4

Minimum value:

Where Z(0.1) = -1.282

Maximum value:

Z(0.9)= 1.282

Given a normal distribution with μ=53 and σ=3.
a. What is the probability that X>49? P(X>49)=_____
(Round to four decimal places as needed.)
b. What is the probability thatX<47?
P(X<47)equals=_____ (Round to four decimal places as
needed.)
c. For this distribution, 7% of the values are less than what
X-value? X=_____ (Round to the nearest integer as needed.)
d. Between what two X-values (symmetrically distributed around
the mean) are 80% of the values? For this distribution, 80% of
the values...

for a normal distribution with mean 100 and standard deviation
of 20, calculate: a) the percentage of the values between 100 and
120 b) the percentage of the values between 60 and 80 c) the
percentage of the values between 80 and 140

The mean of a normal probability distribution is 380; the
standard deviation is 10.
a. About 68% of the observations lie between what two
values?
About 95% of the observations lie between what two values?
Practically all of the observations lie between what two
values?

Given X with a normal distribution with mean 39.5 and standard
deviation 5.0.
a. What is the probability that X is between 38.0 and 42.5?
b. What value of X falls at the 85th percentile?

1. Let the mean be 100 and the standard deviation be 15 for the
normal distribution for adult IQs in North Carolina.
a. Use the empirical rule to find what proportion of the data is
located between 85 and 115.
b. How about 100 and 130?
c. Find the z-score for the following data points and explain
what these mean: i. x = 80 ii. x = 109

A distribution of values is normal with a mean of 46.9 and a
standard deviation of 32.2. Find the probability that a randomly
selected value is between 8.3 and 50.1. P(8.3 < X < 50.1)
=

Consider a normal distribution, with a mean of 75 and a standard
deviation of 10. What is the probability of obtaining a value:
a. between 75 and 10?
b. between 65 and 85?
c. less than 65?
d. greater than 85?

The mean of a normal probability distribution is 380; the
standard deviation is 18. a. About 68% of the observations lie
between what two values? b. About 95% of the observations lie
between what two values? c. Practically all of the observations lie
between what two values?

A distribution of values is normal with a mean of 278.8 and a
standard deviation of 18.6.
Find the probability that a randomly selected value is between
261.7 and 301.9.
P(261.7 < X < 301.9) =
*please show all calculations and steps*

The mean of a normal probability distribution is 340; the
standard deviation is 20.
About 68% of the observations lie between what two values?
About 95% of the observations lie between what two values?
Practically all of the observations lie between what two
values?

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