Lesson Example Discussion Quiz: Class Homework |
Step-2 |
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 |
For a certain type of computers, the length of time bewteen charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours. |
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2 |
Formula: |
\$Z = (X-\mu )/ \sigma\$ |
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3 |
Step |
From the given data |
\$\mu = 50 , \sigma = 15 , X_1 = 50, X_2 = 70\$ |
4 |
Clue |
Probability that the length of time will be between 50 and 70 hours. |
P(50<X<70) |
5 |
Step |
Converting to standard normal curve |
\$P(50<X<70) = (50-50)/ 15 < P((X-\mu )/ \sigma) < (70-50)/ 15)\$ \$P(50<X<70) = P(0<Z<1.33)\$ |
6 |
Step |
P(0<Z<1.33) |
[area to the left of z=1.33] - [area to the left of z=0] |
7 |
Hint |
Take the values from the standard normal distribution table or chart |
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8 |
Step |
P(0<Z<1.33) |
0.9082 - 0.5 |
9 |
Step |
P(0<Z<1.33) |
0.4082 |
10 |
Step |
Probability that the length of time will be between 50 and 70 hours |
0.4082 |
11 |
Answer |
B |
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Tutor: Questions
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Problem |
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3 |
Hint |
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4 |
Step |
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5 |
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