Need help with only d According to one association, the total energy needed during pregnancy is normally distributed, withmean 2600 and standard deviation 50.(a) Is total energy needed during pregnancy a qualitative variable or a quantitative variable?(b) What is the probability that a randomly selected pregnant woman has an energy need of more than2625?(c) Describe the sampling distribution of X, the sample mean daily energy requirement for a randomsample of 20 pregnant women.1(d) What is the probability that a random sample of 20 pregnant women has a mean energy need ofmore than 2625?102#A3Q$423%A5#tvMacBook Pro6&7.8A(9(10(×104

Suppose the random variable x defines the total energy needed during pregnancy by a woman.It is given that; x follows a normal distribution with mean of µ = 2600 and the standard deviation of σ = 50.The sample mean is denoted as x̄. The sample size is n = 20.The sample size is not large (< 30). However, the population is normally distributed.Thus, according to the central limit theorem, the mean of the sampling distribution of the sample mean is, µx̄ = µ = 2600.According to the central limit theorem, the standard deviation of the sampling distribution of the sample mean is, σx̄ = σ/√n = 50/√20 = 11.18033989.According to the Central Limit Theorem, x̄ is approximately normal with a mean of 2600 and a standard deviation of 11.18033989.The z score formula is, z = (x̄ – µx̄)/σx̄.The probability that a random sample of 20 pregnant women has a mean energy need of more than 2625 is, The excel output is, Thus, the probability that a random sample of 20 pregnant women has a mean energy need of more than 2625 is 0.0127.The probability that a random sample of 20 pregnant women has a mean energy need of more than 2625 is 0.0127.