The assembly times for a toy car follow a normal distribution with a mean of 55 minutes and a standard deviation of 4 minutes. The company closes at 5pm every day. If one worker starts to assemble a toy car at 4pm, what is the probability that she will finish this job before the company closes for the day?
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To find the probability that the worker will finish assembling the toy car before the company closes, we need to calculate the Z-score and then look up the corresponding area under the standard normal curve.
1. Calculate the Z-score:
The Z-score measures how many standard deviations the assembly time is from the mean. It can be calculated using the formula:
Z = (X - μ) / σ
where X is the given time (in this case, 60 minutes), μ is the mean assembly time (55 minutes), and σ is the standard deviation (4 minutes).
Z = (60 - 55) / 4
Z = 5 / 4
Z = 1.25
2. Look up the area under the standard normal curve corresponding to the calculated Z-score.
You can use a Z-table or a calculator to find the area. By looking up the Z-score of 1.25 in a Z-table, you'll find that the area to the left of this Z-score is approximately 0.8944.
3. Calculate the probability:
The probability of finishing before the company closes is the same as the area under the standard normal curve to the left of the Z-score. Thus, the probability is approximately 0.8944 or 89.44%.
Therefore, the probability that the worker will finish assembling the toy car before the company closes is approximately 0.8944 or 89.44%.