See , unless and until we are not told it follows standard normal distribution which relies on finding Z score , we should not do so..We should follow properties of general normal distribution..
According to the question we are considering data about mean = 0.900
And value of one standard deviation = ∓ 0.003
But the error mentioned is = ∓ 0.005
which is hence within 2 standard deviations of given data distribution..
We know ,
P(μ - σ <= x <= μ + σ) = 0.68
P(μ - 2σ <= x <= μ + 2σ) = 0.95
P(μ - 3σ <= x <= μ + 3σ) = 1 , where
μ : Mean of normal distribution
σ : Standard deviation of normal distribution
For standard normal distribution ,
μ : 0 and σ : 1 and z = (x - μ) / σ
So as here it is normal distribution we need not find z score..As we can see ,
It follows the 2nd case i.e. under 2 standard deviations but not 1 standard deviation..
Hence the probabiltiy is approximately 0.95 as error limit given is 0.005 but 2 σ = 0.006..
Hence A) is the correct answer..