The time to complete the construction of a scaption derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it wesild take between 2.5 and 3.5 hours to construct a soapbox derby car
06915
0.3085
04170
0.3830
To find the probability that it takes between 2.5 and 3.5 hours to construct a soapbox derby car, we can calculate the area under the normal distribution curve between these two values.
First, we calculate the z-scores for both 2.5 and 3.5 hours using the formula:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
For 2.5 hours:
z = (2.5 - 3) / 1 = -0.5
For 3.5 hours:
z = (3.5 - 3) / 1 = 0.5
Next, we use a standard normal distribution table (or a calculator) to find the area under the curve between these z-scores.
Looking up the z-scores in the table, we find that the area to the left of -0.5 is 0.3085, and the area to the left of 0.5 is 0.6915. Subtracting the smaller area from the larger area gives us:
0.6915 - 0.3085 = 0.3830
Therefore, the probability that it takes between 2.5 and 3.5 hours to construct a soapbox derby car is approximately 0.3830.