Answer:
So, the probability is P=0.27.
Step-by-step explanation:
We know that the mean of computer chips is 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.
We get:
[tex]n=12\\\\\mu=1\\\\\sigma=0.1\\[/tex]
We calculate:
[tex]z=\frac{(0.99-1)\cdot \sqrt{12}}{0.1}=-0.35\\\\z=\frac{(1.01-1)\cdot \sqrt{12}}{0.1}=0.35[/tex]
We use a table for standard normal distribution, and we calculate the probability:
[tex]P(0.99<x<1.01)=P(-0.35<z<0.35)\\\\P(0.99<x<1.01)=P(z=0.35)-P(z=-0.35)\\\\P(0.99<x<1.01)=0.63-0.36\\\\P(0.99<x<1.01)=0.27\\[/tex]
So, the probability is P=0.27.
The probability that the sample mean will be between 0.99 and 1.01 centimeters is 26.62%
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / (standard deviation÷√sample size)
Given; mean of 1 cm, standard deviation of 0.1 cm, sample = 12
a) For 0.99:
z = (0.99 - 1)/(0.1 ÷ √12) = -0.34
For 1.01:
z = (1.01 - 1)/(0.1 ÷ √12) = 0.34
P(0.34 < z < -0.34) = P(z < 0.34) - P(z < -0.34) = 0.6331 - 0.3669 = 0.2662
The probability that the sample mean will be between 0.99 and 1.01 centimeters is 26.62%
Find out more on z score at: https://brainly.com/question/25638875
