Concrete blocks are produced in lots of 2000. Each block has probability 0.85 of meeting a strength specification. The blocks are independent. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. What is the probability that, in a given lot, fewer than 1690 blocks meet the specification?

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