Applying Normal Distribution to Real-World Data Quiz

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| Questions: 20 | Updated: Nov 16, 2025
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1) What is the z-score for a day with a high of 90°F?

Explanation

(90−78)/6 = 2.0

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About This Quiz
Applying Normal Distribution To Real-world Data Quiz - Quiz

This quiz applies your understanding of the normal distribution to real-world contexts. You’ll use z-scores to analyze various data sets, such as daily temperatures, SAT scores, or factory production rates, to calculate proportions and make decisions based on normal distribution parameters.

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2) Approximately what proportion of June days have highs above 90°F?

Explanation

For z = 2, the upper-tail area ≈ 0.0228

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3) What temperature corresponds to the 84th percentile of the distribution?

Explanation

84th percentile ≈ z = 1 → 78 + (1×6) = 84°F

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4) On what percentage of days do highs fall between 72°F and 84°F?

Explanation

Between ±1 standard deviation ≈ 68%

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5) A restaurant plans extra patio staff on the hottest 10% of days. What temperature threshold should they use?

Explanation

90th percentile z ≈ 1.28 → 78 + (1.28×6) = 85.7°F

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6) Two separate weeks had average highs of 79°F and 83°F with the same day-to-day SD of 6°F. Which week was more unusually warm relative to June’s distribution?

Explanation

(83−78)/6 = 0.83 → higher z means more unusual

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7) What is the z-score for a student who scored 680?

Explanation

(680−520)/110 ≈ 1.45 ≈ 1.6

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8) Approximately what percent of students score below 680?

Explanation

For z ≈ 1.6, cumulative area ≈ 94.5%

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9) What score marks the top 5%?

Explanation

95th percentile z ≈ 1.645 → 520 + (1.645×110) ≈ 701

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10) The middle 50% of scores are between which two values (approx.)?

Explanation

Q1, Q3 at z = ±0.674 → 520 ± (0.674×110) ≈ 446–594

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11) A school recognizes students in the top 10%. What is the minimum qualifying score?

Explanation

90th percentile z ≈ 1.28 → 520 + (1.28×110) ≈ 661

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12) What proportion of rods are shorter than 98.5 mm?

Explanation

z = (98.5−100)/0.8 = −1.875 → area ≈ 0.0228

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13) What proportion of rods are within spec (between 98.5 mm and 101.5 mm)?

Explanation

Between z = ±1.875 → ≈ 0.94 of all rods

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14) The factory wants at most 0.3% out-of-spec on the high side. What max mean shift (by magnitude) can they tolerate if SD stays 0.8 mm and the upper spec is 101.5 mm?

Explanation

z ≈ 2.75 for 0.3% tail → (101.5−mean)/0.8 = 2.75 → shift ≈ 0.7 mm

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15) If the standard deviation increases to 1.2 mm while the mean stays 100 mm, what is the new proportion above 101.5 mm?

Explanation

z = (1.5/1.2) = 1.25 → area above ≈ 0.1056

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16) What proportion of adult males are taller than the doorway?

Explanation

z = (76−70)/3 = 2 → upper tail ≈ 0.0228

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17) What height corresponds to the 25th percentile?

Explanation

25th percentile z = −0.674 → 70 − (0.674×3) ≈ 68 in

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18) A basketball team recruits from the tallest 2.5% of men. What is the minimum height?

Explanation

z = 1.96 → 70 + (1.96×3) ≈ 75.9 in

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19) Two friends are 74 inches and 65 inches tall. Who is more unusual relative to the distribution?

Explanation

|−1.67| > |1.33| → 65 in is more unusual

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20) A clothing brand designs pants to fit the middle 80% of men by height. What range should they target?

Explanation

Middle 80% → z = ±1.28 → 70 ± (1.28×3) = 66.2–73.8 in

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What is the z-score for a day with a high of 90°F?
Approximately what proportion of June days have highs above 90°F?
What temperature corresponds to the 84th percentile of the...
On what percentage of days do highs fall between 72°F and 84°F?
A restaurant plans extra patio staff on the hottest 10% of days. What...
Two separate weeks had average highs of 79°F and 83°F with the same...
What is the z-score for a student who scored 680?
Approximately what percent of students score below 680?
What score marks the top 5%?
The middle 50% of scores are between which two values (approx.)?
A school recognizes students in the top 10%. What is the minimum...
What proportion of rods are shorter than 98.5 mm?
What proportion of rods are within spec (between 98.5 mm and 101.5...
The factory wants at most 0.3% out-of-spec on the high side. What max...
If the standard deviation increases to 1.2 mm while the mean stays 100...
What proportion of adult males are taller than the doorway?
What height corresponds to the 25th percentile?
A basketball team recruits from the tallest 2.5% of men. What is the...
Two friends are 74 inches and 65 inches tall. Who is more unusual...
A clothing brand designs pants to fit the middle 80% of men by height....
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