Answer:
Step-by-step explanation:
Let x be the random variable representing the time (in minutes) taken for a dose of a certain drug to be effective as a sedative on lab animals. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 1
σ = √variance = √0.01 = 0.1
the probability that the time taken for a randomly selected animal is between 1 and 1.1 minutes is expressed as
P(1 ≤ x ≤ 1.1)
For x = 1,
z = (1 - 1)/0.1 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 1.1
z = (1.1 - 1)/0.1 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
Therefore,
P(1 ≤ x ≤ 1.1) = 0.84 - 0.5 = 0.34
The the proportion of animals for which the time taken is between 1 and 1.1 minutes is 0.34
