Question

Given a normal distribution with mean of 100 and standard deviation of 10, what is the probability that:

a. X > 80?

b. X < 65?

c. X < 75 or X > 90?

d. Between what two X values (symmetrically distributed around the mean) are ninety percent of the values

Answer #1

a.

X ~ N(100, 10^{2})

P(X > 80) = P[Z > (80 - 100)/10] = P[Z > -2] = 0.9772

b.

P(X < 65) = P[Z < (65 - 100)/10] = P[Z < -3.5] = 0.0002

c.

P(X < 75 or X > 90) = P(X < 75) + P(X > 90)

= P[Z < (75 - 100)/10] + P[Z > (90 - 100)/10]

= P[Z < -2.5] + P[Z > -1]

= 0.0062 + 0.8413

= 0.8475

d.

For ninety percent of the values, the percentiles are (1 - 0.9)/2 and 0.9 + (1 - 0.9)/2 which are 0.05 and 0.95

Z value for p = 0.05 and 0.95 are -1.645 and 1.645

The two values are,

100 - 1.645 * 10 = 83.55

100 + 1.645 * 10 = 116.45

Between 83.55 and 116.45, 90% of the data lies.

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?

Given a normal distribution with μ=100 and σ=10, complete parts
(a) through (d).
a. What is the probability that X>80?
(Round to four decimal places as needed.)
b. What is the probability that X<95?
(Round to four decimal places as needed.)
c. What is the probability that X<75 or X>110?
(Round to four decimal places as needed.)
d. 80% of the values are between what two X-values
(symmetrically distributed around the mean)?
(Round to two decimal places as needed.)

Given a standardized normal
distribution (with a mean of 0 and a standard deviation of 1) what
is the probability that
Z is between -1.23 and 1.64
Z Is less than -1.27 or greater than 1.74
For normal data with values symmetrically distributed around
the mean find the z values that contain 95% of the data
Find the value of z such that area to the right is 2.5% of the
total area under the normal curve

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?

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?

for a normal distribution with mean 100 and standard deviation
10, find the probability of obtaining a value greater than or equal
to 80 but less than or equal to 115. Using excel please.

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) For a sample mean of 70 and a standard deviation of 6 under a
normal distribution, find:
a) The % of data values below 72
b) The % of data values between 65 and 75
c) The % of data values above 80

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 6 minutes ago

asked 6 minutes ago

asked 13 minutes ago

asked 17 minutes ago

asked 39 minutes ago

asked 39 minutes ago

asked 42 minutes ago

asked 52 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago