Question

The time for a super glue to set can be treated as a random variable having a normal distribution with mean 30 second. Find its standard deviation if the probability is 0.20 that it will take on a value greater than 39.2 seconds.

Answer 1

Using the provided mean setting time and the probability of a longer setting time, the calculation results in an approximate standard deviation of 10.93 seconds for the super glue's setting time.

Step-by-step explanation:

To find the standard deviation of the super glue's setting time, we use the information that the mean is 30 seconds and the probability of the setting time being greater than 39.2 seconds is 0.20. First, we find the z-score corresponding to the 0.20 probability in the upper tail of the normal distribution. Using the standard normal distribution table, this z-score is approximately 0.8416 since 1-0.20 = 0.80. The z-score formula is:
Z = (X - μ) / σ
where μ is the mean, σ is the standard deviation, and X is the value. Plugging the values we have:
0.8416 = (39.2 - 30) / σ
Solving for σ gives us:

σ = (39.2 - 30) / 0.8416

σ = 9.2 / 0.8416

σ ≈ 10.93 seconds

The standard deviation of the super glue setting time is therefore approximately 10.93 seconds.