CAIE S1 2015 June — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeFind mean from probability statement
DifficultyModerate -0.8 This is a straightforward inverse normal problem requiring a single standardization and rearrangement. Students need only look up z = 1.15 (for upper tail 0.128), then solve 195 = μ + 1.15(22), which is routine application of the normal distribution formula with no conceptual challenges.
Spec2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation
1 The weights, in grams, of onions in a supermarket have a normal distribution with mean \(\mu\) and standard deviation 22. The probability that a randomly chosen onion weighs more than 195 grams is 0.128 . Find the value of \(\mu\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(z = 1.136\)B1 \(\pm 1.136\) seen, not \(\pm 1.14\)
\(1.136 = \frac{195 - \mu}{22}\)M1 Standardising, no cc no sq rt, equated to their \(z\) not 0.128 or 0.872
\(\mu = 170\)A1 [3] Correct answer, nfww 
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $z = 1.136$ | B1 | $\pm 1.136$ seen, not $\pm 1.14$ |
| $1.136 = \frac{195 - \mu}{22}$ | M1 | Standardising, no cc no sq rt, equated to their $z$ not 0.128 or 0.872 |
| $\mu = 170$ | A1 **[3]** | Correct answer, nfww |

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1 The weights, in grams, of onions in a supermarket have a normal distribution with mean $\mu$ and standard deviation 22. The probability that a randomly chosen onion weighs more than 195 grams is 0.128 . Find the value of $\mu$.

\hfill \mbox{\textit{CAIE S1 2015 Q1 [3]}}
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