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Chapter 6: Q. 25 (page 385)

Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?

Short Answer

Expert verified

The value of thezscore is-0.33

Step by step solution

01

Given information

Given in the question that, a normal distribution has a mean of six and a standard deviation of 1.5

The value of x=5.5

We have to find the value ofzscore

02

Explanation 

According to the given information,

X~N(6,1.5)

Where,

渭=6

蟽=1.5

x=5.5

We can compute the zscore value as follow:

z=x鈭�渭蟽

Place the given values in the above equation:

z=5.5鈭�61.5

=鈭�0.51.5

鈮�鈭�0.33

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Most popular questions from this chapter

a. Suppose a 15 to 18-year-old male from Chile was 176cm tall from 2009to 2010. The z-score when x=176 cm isz= _______. This z-score tells you that x=176cm is ________ standard deviations to the ________ (right or left) of the mean _____ (What is the mean?). b. Suppose that the height of a 15 to 18-year-old male from Chile from2009 to 2010 has a z-score of z=鈥�2. What is the male鈥檚 height? The z-score(z=鈥�2) tells you that the male鈥檚 height is ________ standard deviations to the __________ (right or left) of the mean.

How would you represent the area to the left of one in a probability statement?

Suppose X ~ N(9, 5). What value of x has a z-score of 鈥�0.5?

If the area to the right of x in a normal distribution is 0.543, what is the area to the left ofx?

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66inches and a standard deviation of 2.5inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

a.X~_____(_____,_____)

b. Find the probability that the person is between 65and 69inches. Include a sketch of the graph, and write a probability statement.

c. Would you expect to meet many Asian adult males over 72 inches? Explain why or why not, and justify your answer numerically.
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