Respuesta :
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
The probability that, in a given lot, fewer than 1690 blocks meet the specification is 0.2644.
Given
Concrete blocks are produced in lots of 2000.
Each block has a probability of 0.85 of meeting a strength specification.
The blocks are independent.
What is the formula to calculate z-score?
The formula is used to calculate z-score is;
[tex]\rm z-score = \dfrac{X-mean \ value }{Standard \ deviation}[/tex]
The standard deviation is given by;
[tex]\rm Standard \ deviation = \sqrt{npq}\\\\Standard \ deviation=\sqrt { n \times p \times (1-p)}\\\\Standard \ deviation=\sqrt { 2000 \times 0.85 \times (1-0.85)}\\\\ Standard \ deviation=\sqrt { 2000 \times 0.85 \times 0.15}\\\\ Standard \ deviation=\sqrt { 255}\\\\Standard \ deviation=15.95[/tex]
Then,
The z-value is;
[tex]\rm z-score = \dfrac{X-mean \ value }{Standard \ deviation}\\\\\rm z-score = \dfrac{1690-1700 }{15.95}\\\\\rm z-score = \dfrac{-10}{15.95}\\\\\rm z-score = -0.63[/tex]
Therefore,
The normal distribution table for the corresponding z-score is 0.2644.
Hence, the probability that, in a given lot, fewer than 1690 blocks meet the specification is 0.2644.
To know more about z-score click the link is given below.
https://brainly.com/question/13299273
