The checker accepts an incorrect answer, although 0.0098 should be the correct answer.

import scipy.stats as st import math

pop_mean = 205 pop_sd = 15 sample_size = 49 x = 9800/49

sample_sd = pop_sd/math.sqrt(sample_size)

z_score = (x-pop_mean)/sample_sd

prob = st.norm.cdf(z_score)

print( '{:0.4f}'.format(prob))

The central limit theorem states that for a large number of independent random variables, the mean of their sum will approach the mean of the sum of the individual random variables as the number of random variables increases.

• weight of each box(X) = 9800 / 49 = 200
• u = 205
• sigma = 15
• n = 49
• sample_sigma = 15/7 = 2.1428
• prob(X < 200) = 200-205 / 2.1428 = -2.33
• z(X < 2.33) = 1 - 0.99010 = 0.0099

p(xmean<=200)=P(Z<=(200-205)/(15/7))=P(Z<=-7/3) and find the corresponding probability in R pnorm(-7/3) is 0.0098