Answer:
a) 21.2%
b) $176.05 or more
c) 15.87%
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $155
Standard Deviation, σ = $25
We are given that the distribution of spending amounts is a bell shaped distribution that is a normal distribution.
Formula:
a) P(spends more than $175 per week on groceries)
P(x > 175)
Calculation the value from standard normal z table, we have,
b) P(X > x) = 0.2
We have to find the value of x such that the probability is 0.2
P(X > x)
Calculation the value from standard normal z table, we have,
A consumer has to spend approximately $176.05 or greater to be in the top 20% of the distribution.
c) My family spends on average $130 dollars on groceries.
P(less than $130)
Calculation the value from standard normal z table, we have,
Thus, my family percentile is 15.87%