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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have