Lesson Example Discussion Quiz: Class Homework |
Step-1 |
Title: Normal distribution |
Grade: 9-a Lesson: S4-L9 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr? |
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2 |
Formula: |
\$Z = (X-\mu )/ \sigma\$ |
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3 |
Step |
From the given data |
\$\mu = 90 , \sigma = 10 , X = 100\$ |
4 |
Clue |
Probability that a car picked at random is travelling at more than 100 km/hr |
P(X>100) |
5 |
Step |
Converting to standard normal curve |
\$P(X>100) = P((X-\mu )/ \sigma) > (100-90 )/ 10)\$ \$P(X>100) = P(Z>1)\$ |
6 |
Step |
P(Z>1) |
[Total area] - [area to the left of z=1] |
7 |
Hint |
Take the values from the standard normal distribution table or chart |
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8 |
Step |
P(Z>1) |
1 - 0.8413 |
9 |
Step |
P(Z>1) |
0.1587 |
10 |
Step |
Probability that a car picked at random is travelling at more than 100 km/hr |
0.1587 |
11 |
Answer |
C |
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Tutor: Questions
| Seq | Type | Question | Audio |
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1 |
Problem |
What did you learn from this problem? |
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2 |
Clue |
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3 |
Hint |
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4 |
Step |
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5 |
Step |
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