Question

The time it takes a cell to divide (mitosis) follows a normal distribution with an average time of one hour and a standard deviation of 5 minutes. Calculate the probability that a cell takes less than 55 minutes to divide.

Answer 1

The probability that a cell takes less than 55 minutes to divide is roughly 15.87%, calculated using the Z-score which is found to be -1 when the mean time is 60 minutes and the standard deviation is 5 minutes.

Step-by-step explanation:

The probability that a cell takes less than 55 minutes to divide, given that the time for cell division follows a normal distribution with a mean of one hour (60 minutes) and a standard deviation of 5 minutes, can be calculated using the Z-score formula:

Z = (X - µ) / σ

Where X is the time of interest (55 minutes), µ is the mean (60 minutes), and σ is the standard deviation (5 minutes). Plugging in the values we get:

Z = (55 - 60) / 5 = -5 / 5 = -1

The Z-score of -1 corresponds to a probability of 0.1587 (or 15.87%) when looking up the value in standard normal distribution tables or using a normal distribution calculator. Therefore, the probability that a cell takes less than 55 minutes to divide is roughly 15.87%.