   # A normal distribution has a mean of μ = 54 and standard deviation of σ = 6. What is the probability of randomly selecting a score less then X = 51? 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? ### Essentials of Statistics for The B...

9th Edition
Frederick J Gravetter + 2 others
Publisher: Cengage Learning
ISBN: 9781337098120

#### Solutions

Chapter
Section ### Essentials of Statistics for The B...

9th Edition
Frederick J Gravetter + 2 others
Publisher: Cengage Learning
ISBN: 9781337098120
Chapter 7, Problem 12P
Textbook Problem
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## A normal distribution has a mean of μ = 54 and standard deviation of σ = 6.What is the probability of randomly selecting a score less then X = 51?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?

a.

To determine

The probability of randomly selecting a score less than X=51 from given population.

### Explanation of Solution

Population mean is μ=54.

Population standard deviation is σ=6.

Random score given is X=51.

Calculation:

If μ and σ represents the population mean and standard deviation respectively. Then,

μ=54σ=6

Let X represents the random score from given population. Let p represents the probability that random score is less than 51.

p=P(X<51)

Software procedure:

Step-by-step procedure to obtain the P(X<51) using the SPSS software:

• Click on first empty block of data view

b.

To determine

The probability of selecting a sample of n=4  with a mean less than M=51 for given distribution.

c.

To determine

The probability of selecting a sample of n=36  with a mean less than M=51 for given distribution.

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