Question

For a normal distribution with a mean of u = 60 and a standard deviation of o = 10,

find the proportion of the population corresponding to each of the following.

a. Scores greater than 65.

b. Scores less than 68.

c. Scores between 50 and 70.

Answer #1

Solution :

Given that ,

mean = = 60

standard deviation = = 10

a) P(x > 65) = 1 - p( x< 65)

=1- p P[(x - ) / < (65 - 60) / 10]

=1- P(z < 0.5)

Using z table,

= 1 - 0.6915

= 0.3085

b) P(x < 68) = P[(x - ) / < (68 - 60) /10 ]

= P(z < 0.8)

Using z table,

= 0.7881

c) P(50 < x < 70) = P[(50 - 60)/10 ) < (x - ) / < (70 - 60) / 10) ]

= P(-1 < z < 1)

= P(z < 1) - P(z < -1)

Using z table,

= 0.8413 - 0.1587

= 0.6826

A normal distribution has a mean of u = 54 and a
standard deviation of o = 6.
a. What is the probability of randomly selecting a
score less than X = 51?
b. What is the probability of selecting a sample of
n = 4 scores with a mean less than M = 51?
c. What is the probability of selecting a sample of
n = 36 scores with a mean less than M = 51?
Show your work

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?

A normal distribution has a mean of 60 and a standard deviation
of 16. For each of the following scores, indicate whether the body
is to the right or the left of the score and find the proportion of
the distribution located in the body X = 64 X = 80 X = 52 X =
28

Given a Normal distribution with a mean (µ) of 60 and standard
deviation (ᵟ) of 8, what is the probability that the sample mean
(Xbar) is:
Less than 57?
Between 57and 62.5?
Above 65?
There is a 38% chance that the Xbar is above what value?

A population has a mean of u = 60 and a standard
deviation of o = 12
a. For this population, find the z-score for each of
the following X values.
X = 69 X = 84 X = 63
X = 54 X = 48 X = 45

1. A distribution of values is normal with a mean of 70.8 and a
standard deviation of 50.9.
Find the probability that a randomly selected value is less than
4.6.
P(X < 4.6) =
2. A distribution of values is normal with a mean of 66 and a
standard deviation of 4.2.
Find the probability that a randomly selected value is greater than
69.4.
P(X > 69.4) =
Enter your answer as a number accurate to 4 decimal places. Answers...

a
normal distribution has a mean of u=65 and a standard deviation of
o= 20. Complete the z score for the sample mean and determine
whether the sample mean is a typical, representative value or an
extreme value for a sample of its size if M= 74 for a sample of 4
score.

a
normal distribution has a mean of u=65 and a standard deviation of
o= 20. Complete the z score for the sample mean and determine
whether the sample mean is a typical, representative value or an
extreme value for a sample of its size if M= 74 for a sample of 4
score.

The mean of a normally distributed data set is 112, and the
standard deviation is 18.
a) Use the Empirical Rule to find the probability
that a randomly-selected data value is greater than 130.
b) Use the Empirical Rule to find the probability
that a randomly-selected data value is greater than 148.
A psychologist wants to estimate the proportion of people in a
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a population with a mean of 65 and a standard deviation of 6 is
being standardized to produce a set of scores with a mean of 50 and
a new standard deviation of 10. find the new standardized values
for each of the following scores from the original distribution
68,59,77,56

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