Common Core Standard HSS-ID.A.4 Questions

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Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following best defines a standard normal distribution?

A normal distribution with [math]mu = 0[/math] and [math]sigma =1[/math].
A normal distribution with [math]mu = 1[/math] and [math]sigma = 0[/math].
A normal distribution with [math]mu=1[/math] and [math]sigma=1[/math].
A normal distribution with [math]mu = 0[/math] and [math]sigma = 0[/math].

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following is true about the mean, median, and mode of a normal distribution?

They are all equal.
The mean and median are always equal, but the mode is either greater or less than them.
The mode and median are always equal, but the mean is usually less than them.
They may or may not be equal; there is no general rule.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

[math]X[/math] is a normally distributed random variable, with a mean of 44 and variance of 13. If just over 8% of the values of the distribution are less than [math]x_0[/math] or greater than [math]x_1[/math], determine [math]x_0[/math] and [math]x_1[/math] to the nearest tenth. Assume that an equal percentage of the values of the distribution are less than [math]x_0[/math] as are greater than [math]x_1[/math].

21.3 and 66.8
-64 and 90
25.7 and 62.3
42.7 and 45.3

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Human pregnancies are normally distributed, with a mean of 266 days and a standard deviation of 16 days. A doctor is interested in studying the 4% least likely pregnancy lengths (either very short or very long). What length of pregnancies should she consider for a very short or very long pregnancy? Round the answer to the nearest day.

264 and 268 days
238 and 294 days
233 and 299 days
255 and 277 days

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

What does a z-score indicate about a given data point (or raw score) from a normal distribution?

The probability that the data point will occur.
The percentile in which the data point lies.
The number of standard deviations away from the mean the data point lies.
The frequency of the data point.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which parameters are needed to define a normal distribution?

The mean and the standard deviation.
The mean alone.
The range and the mean.
The range, standard deviation, and IQR.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

A random variable [math]X[/math] is normally distributed with a mean of 17 and standard deviation of 4.5. The probability that [math]X[/math] is greater than 17 but less than [math]x_0[/math] is 17%. What is the value of [math]x_0[/math], rounded to the nearest tenth (if necessary)?

0.4
19.0
21.3
15.0

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following is/are true for the standard normal distribution? Choose all correct answers.

34% of the values are between 0 and 1.
95% of the values are between -2 and 2.
About 50% of the values are less than 6.
About 100% of the values are greater than -7.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

The graph of a normal distribution is plotted. However, the standard deviation used was incorrect. The actual standard deviation is larger than what was used. What will happen to the shape of the graph?

It will become narrower and taller.
It will become wider and shorter.
It will become wider and taller.
It will become narrower and shorter.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

The random variable [math]X[/math] has a normal distribution with a mean of -5 and standard deviation of 1.1. If the probability that [math]X[/math] is greater than [math]x_0[/math] but less than the mean is about 25.5%, determine the value of [math]x_0[/math] to the nearest tenth.

-5.8
-2.4
-4.2
4.2

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following best defines a z-table?

A table which gives the probabilities of various z-scores occurring.
A table which gives the probabilities of various z-scores being less than or greater than the mean.
A table which gives the percentage of values within one standard deviation of a certain z-score.
A table which gives the percentage of values between 0 (or positive/negative infinity) and a certain z-score.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

A large group of data is normally distributed, with [math]mu = 46[/math] and [math]sigma = 9[/math]. What is the probability of a value of 48 or less?

58.71%
41.29%
8.71%
74.54%

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

[math]X[/math] is a normally distributed random variable with mean 77 and standard deviation 15. If the probability that [math]X[/math] is less than [math]x_0[/math] and greater than 97.25 is about 5%, what is the value of [math]x_0[/math], rounded to one decimal?

50.8
52.4
93.4
103.6

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following is the formula for calculating the z-score of a value of [math]x[/math], where [math]x[/math] is a value (or raw score) from a set of normally distributed data? Let [math]mu[/math] be the population mean and [math]sigma[/math] be the population standard deviation of this data.

[math]z = x/sigma[/math]
[math]z = x - mu/sigma[/math]
[math]z = (x - mu)/sigma[/math]
[math]z = sqrt((x-mu)/sigma)[/math]

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

The random variable [math]X[/math] is normally distributed, with a mean of 90 and standard deviation of 10. What is the probability that [math]X[/math] is less than 81?

81.59%
31.59%
46.41%
18.41%

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

The random variable [math]X[/math] has a normal distribution with [math]mu=45[/math] and [math]sigma=9.5[/math]. If [math]P(x_0 <= X <= x_1) ~~ 82%[/math], determine [math]x_0[/math] and [math]x_1[/math] to one decimal place. Assume that [math]mu - x_0 = x_1 - mu[/math].

46.8 and 51.2
40.3 and 106.0
-8 and 57.7
32.3 and 57.7

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following is true about calculating a z-score for data which is not normally distributed?

There is no difference from normally distributed data.
Although it can be computed, it may not have a typical (or any useful) meaning.
It can be computed, but the formula is slightly different (one takes the square root of the usual z-score).
It is impossible to compute the z-score for non-normally distributed data.

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

A large group of data is normally distributed with a mean of 67 and standard deviation of 14. What percentage of the data is above 95?

97.72%
47.72%
2.28%
28.77%

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

A random variable [math]X[/math] is normally distributed with a mean of 10 and standard deviation of 2.6. The probability that [math]X[/math] lies between [math]x_0[/math] and [math]x_1[/math] is just under 60%. Also, the probability that [math]X[/math] is less than [math]x_0[/math] is about 10%. Determine the values of [math]x_0[/math] and [math]x_1[/math], to the nearest tenth.

7.8 and 12.2
6.7 and 11.4
6.7 and 13.3
8.6 and 11.4

Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4

Which of the following is true concerning z-scores?

Z-scores are always positive.
Z-scores are negative only when the population mean is negative.
Z-scores are positive if the mean is less than the raw score, and negative if the mean is greater than the raw score.
Z-scores are positive if the standard deviation is greater than the raw score, and negative if the standard deviation is less than the raw score.

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Common Core Standard HSS-ID.A.4 Questions

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