Answer:
P(Y ≥ 15) = 0.763
Step-by-step explanation:
Given that:
Mean =135
standard deviation = 12
sample size n = 50
sample mean = 140
Suppose X is the random variable that follows a normal distribution which represents the weekly supermarket expenses
Then,
The probability that X is greater than 140 is :
P(X>140) = 1 - P(X ≤ 140)
From z tables,
Similarly, let consider Y to be the variable that follows a binomial distribution of the no of household whose expense is greater than $140
Then;
∴
P(Y ≥ 15) = 1- P(Y< 15)
P(Y ≥ 15) = 1 - ( P(Y=0) + P(Y=1) + P(Y=2) + ... + P(Y=14) )
P(Y ≥ 15) = 0.763