Answer to Question #167113 in Statistics and Probability for China

Question

4. The height of grade 1 pupils are approximately normally distributed with µ = 45 inches and  = 2. a.      A class of 30 of these pupils is used as a sample. What is the probability that the class mean is between 42 and 47?

Answer 1

$Here,\\ \text{Mean}(\mu)=45\\ \text{Standard Deviation}(\sigma)=2\\ \text{Sample size}(n)=30\\ \text{Lower value of the area}(\bar x_1) = 42\\ \text{Upper value of the area}(\bar x_2)= 47$

We are looking for P(42<$\bar x$ <47)

TI-Calculator:  

normalcdf (lower value of the area, upper value of the area, mean,$\dfrac{\text{Standard Deviation}(\sigma)}{\sqrt n}$ )

The probability that the class mean is between 42 inches and 47 inches is =

TI-Calculator:  normalcdf (42,47,45,0.365)= 0.999999978668

So, The probability that the class mean is between 42 inches and 47 inches is= 0.99