Answer:
Step-by-step explanation:
Let us assume a normal distribution
The formula for normal distribution is
z = (x - u)/s
Where
u = mean = np
s = standard deviation = √npq
x = number of blocks that meet the specification
n = number of blocks sampled
From the information given,
p = 0.85 = probability that the block will meet the strength specification.
q = 1 - p = 1 - 0.85 = 0.15 = probability that the block will not meet the strength specification.
n = 2000
u = np = 2000 × 0.85 = 1700
s = √npq = √1700×0.15 = 15.97
We want to find the P(x lesser than 1690). It becomes
z = (1690 - 1700)/15.97
z = -10/15.9 = -0.63
Looking at the normal distribution table for the corresponding z score, it is 0.2644
Therefore
P(x lesser than 1690) = 0.2644
