Question

# Given a population with a mean of µ = 100 and a variance σ2 = 12,...

Given a population with a mean of µ = 100 and a variance σ2 = 12, assume the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 52 is obtained. What is the probability that   98.00 < x < 100.76?

the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean of the sampling distribution ( x ) = 100
standard Deviation ( sd )= 12/ Sqrt ( 52 ) =1.6641
sample size (n) = 52

the probability that 98.00 < x < 100.76
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 98) = (98-100)/12/ Sqrt ( 52 )
= -2/1.6641
= -1.2019
= P ( Z <-1.2019) From Standard Normal Table
= 0.1147
P(X < 100.76) = (100.76-100)/12/ Sqrt ( 52 )
= 0.76/1.6641 = 0.4567
= P ( Z <0.4567) From Standard Normal Table
= 0.6761
P(98 < X < 100.76) = 0.6761-0.1147 = 0.5613

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• Statistics Discussion: The accuracy of a forecasting technique is evaluated especially using the MSE (mean squared...
• If the U.S. government manages to close a recessionary gap and achieve potential GDP with fiscal...
• A block with mass 10kg is on a ramp angled at 20 degrees above the horizontal,...
• I have a sample of 31 7thgrade girls who took an IQ test.  I calculated the sample...
• A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
• Brick column in the external corridor of a house, with section size of 440 mm X520...