Common Core Standard HSS-ID.A.4 Questions

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

For a normal distribution, what percentage of the values are NOT within 3 standard deviations of the mean?

0.3%
3%
5%
10%

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

For the normally distributed random variable [math]X[/math], with [math]mu = -5[/math] and [math]sigma = 1.5[/math], determine [math]P(-4 <= X <= 0)[/math].

99.96%
0.04%
25.14%
25.10%

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

An elite university receives tens of thousands of applications for admittance to a special program at the university each year. For the initial vetting process, the university only looks at about the top 8% of applicants (in terms of composite SAT scores). If the applications for a certain year have a mean SAT score of 1100, with a standard deviation of 250, what is the cutoff SAT score for the first step of the vetting process? Round to the nearest whole number, if necessary.

1125
1150
1538
1453

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

Which of the following is true about the graph of a normal probability distribution? Choose all correct answers.

The curve extends to negative infinity and positive infinity.
The area under the curve equals 1.
The maximum of the curve occurs at a value greater than zero.
The slope of the curve is always positive.

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

The random variable [math]X[/math] is normally distributed with a mean of 58 and standard deviation of 3.5. If just under 35% of the values of this distribution are greater than [math]x_0[/math], what is the value of [math]x_0 ?[/math] Round the answer to one decimal place, if necessary.

0.39
16.5
59.4
61.6

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

A company is looking to hire a contractor to do some work for a short period of time. Each contractor that bids on the job has to provide an estimate of their budget. Many contractors have applied for the job. The mean of the budget estimates is $13,045 with a standard deviation of $308. If the company only wants to look more closely at the the cheapest 15% of the offers, what is the maximum budge estimate that will still get further consideration?

$1,956.75
$12,961.48
$13,084.68
$12,724.68

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

Which of the following is true concerning graphs of normal distributions?

They are never symmetric.
They are symmetric if the mean is greater than the standard deviation.
They are always symmetric about 0.
They are always symmetric about the mean value.

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

A large group of data is normally distributed with a mean of 29 and standard deviation of 1.4. If almost 14% of the data is less than [math]x_0[/math], what is the value of [math]x_0 ?[/math] Round the answer to one decimal place, if necessary.

27.5
28.5
29.5
30.5

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

The town of Cedarbrook has an outdoor market every Saturday. All the vendors keep track of individual sales (how much a person spends at their booth). These sales are normally distributed, with a mean of $38.67 and a standard deviation of $7.55. What percent of people spend within $3.00 of $38.67? Round the answer to the nearest tenth of a percent.

65.5%
31.1%
34.5%
22.1%

Grade 11 Statistics and Probability Concepts CCSS: HSS-ID.A.4

What is the z-value for [math]X = 24[/math] in a set of normally distributed data with [math]µ = 20[/math] and [math]σ = 1.6[/math]?

-4
-2.5
0.4
2.5

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

Which of the following is about a normal distribution?

About half the values are greater than the mean.
Most of the data is less than the mean.
Most of the data is greater than the mean.
More than 90% of the data is greater than the mean plus 2 standard deviations.

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

For the random variable [math]X[/math], which is normally distributed with [math]mu=3[/math] and [math]sigma=0.4[/math], [math]P(X < x_0) ~~ 0.20[/math]. What is the value of [math]x_0 ?[/math] Round the answer to one decimal place.

2.9
-2.1
3.3
2.7

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

Teacher salaries for a certain country are normally distributed, with a mean of $45,600 and a standard deviation of $8,200. What is the probability that a teacher will earn between $50,000 and $55,000?

16.95%
12.51%
29.46%
70.54%

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

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Common Core Standard HSS-ID.A.4 Questions

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