1) A hospital in a large city records the weight of every infant born at the hospital. The distribution of weights is normally distributed, with a mean µ “ 2.9 kilograms and a standard deviation σ = 0.45. Determine the following and attach R code.

(a) The percentage of infants who weighted less than 2.1 kilograms.

(b) The percentage of infants who weighed between 1.8 and 4.0 kilograms.

(c) The percentage of infants who weighed between 3.4 and 4.1 kilograms.

(d) The weight that divides the distribution such that 1% of the weights are above it.

(e) If 15,000 infants have been born at the hospital, approximately how many weighed less than 3.5 kilograms?

2) Suppose a variable is normally distributed. What percentage of scores fall between one standard deviation below the mean and two standard deviations above the mean? Attach R code.