MATH SOLVE

2 months ago

Q:
# In a large population of college-educated adults, the mean IQ is 118 with a standard deviation of 20. Suppose 200 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 120 is ____

Accepted Solution

A:

Answer: 0.0793Step-by-step explanation:Let the IQ of the educated adults be X then;Assume X follows a normal distribution with mean 118 and standard deviation of 20.This is a sampling question with sample size, n =200To find the probability that the sample mean IQ is greater than 120:P(X > 120) = 1 - P(X < 120)Standardize the mean IQ using the sampling formula : Z = (X - μ) / σ/sqrt nWhere; X = sample mean IQ; μ =population mean IQ; σ = population standard deviation and n = sample sizeTherefore, P(X>120) = 1 - P(Z < (120 - 118)/20/sqrt 200) = 1 - P(Z< 1.41)The P(Z<1.41) can then be obtained from the Z tables and the value is 0.9207Thus; P(X< 120) = 1 - 0.9207 = 0.0793