AP Statistics z-Scores and the Normal Distribution Test Solutions and Scoring (PDF)

AP Statistics math test solutions: z-Scores and the Normal Distribution – Maths PDF

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This ap statistics normal distribution test answers for AP Statistics covers z-scores and the normal distribution (Common Core AP STAT 1.10, AP STAT 1.11, HSS-ID.A.4), with a free PDF to print.

Each solution includes a scoring guide. Award points for the correct z-score, the correct area, and the sentence that answers the question in context.

AP Statistics · Common Core State Standards: AP STAT 1.10, AP STAT 1.11, HSS-ID.A.4

Ap statistics normal distribution test answers: worked solutions

Question 1 – z-scores [3 pts]

(a) \(z=\frac{88-70}{10}=1.8\). (b) \(70-5=65\).

1.8; 65; above the mean by 1.8 sd.

Scoring: 1 point per part.

Question 2 – Normal area [3 pts]

Test scores.

z = -1 and z = 2. \(0.9772-0.1587=0.8186\).

0.8186.

Scoring: 1 point for each correct z-score, 1 point for the area.

Question 3 – Empirical rule [2 pts]

600 is 2 standard deviations above the mean. 95% are within 2, so 5% outside, and 2.5% above.

About 2.5%.

Scoring: 1 point for z = 2, 1 point for 2.5%.

Question 4 – Percentile [3 pts]

For area 0.80, \(z=0.84\). \(x=70+0.84(10)=78.4\).

About 78.4: 80% of scores are at or below 78.4.

Scoring: 1 point for the z-score, 1 point for the value, 1 point for the interpretation.

Question 5 – Compare scores [2 pts]

Priya: \(z=1.3\). Diego: \(z=\frac{27-21}{4.5}=1.33\).

Diego (z = 1.33 compared with 1.30).

Scoring: 1 point for each z-score and 1 for the conclusion, 2 points total with partial credit.

Question 6 – Counts from the rule [2 pts]

Bottle volume.

These limits are 1 sd from the mean, so about 68%: \(0.68\times 800=544\).

About 544 bottles.

Scoring: 1 point for 68%, 1 point for 544.

Question 7 – Rejection rate [3 pts]

Bottle volume.

\(z=\frac{11.8-12}{0.15}=-1.33\). \(P(Z < -1.33)=0.0918\).

0.0918.

Scoring: 1 point for z, 1 point for the sketch or setup, 1 point for 0.0918.

Question 8 – Unit change [2 pts]

Mean \(150(0.4536)=68.04\), sd \(20(0.4536)=9.07\).

68.04 kg and 9.07 kg; z-scores do not change.

Scoring: 1 point for the two values, 1 point for the z-score statement.

Total score

Total

20 points

Key facts behind this ap statistics normal distribution test answers

Key facts

z = (x – mean) / sd measures position in standard deviations.
Empirical rule: 68% within 1 sd, 95% within 2 sd, 99.7% within 3 sd.
Area under the curve over an interval is the proportion of values in it; total area is 1.
Use normalcdf for areas and invNorm for percentiles; always sketch and shade first.
A percentile is the percent of values at or below a given value.

How to use this ap statistics normal distribution test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All AP Statistics chapters: AP Statistics math.

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