Example 1: calculation of normal probabilities using and tables of standard normal areas the u. s. department of agriculture (usda), in its official food plans
(), states that the average cost of food for a 14- to 18-year-old male (on the moderate-cost plan) is $261.50 per month. assume that the monthly food
cost for a 14- to 18-year-old male is approximately normally distributed with a mean of $261.50 and a standard deviation of $16.25.
a. use a table of standard normal curve areas to find the probability that the monthly food cost for a randomly selected 14- to 18-year-old male is
i. less than $280.
ii. more than $270.
iii. more than $250.
iv. between $240 and $275.
b. explain the meaning of the probability that you found in part (a)(iv).

i) 0.872

ii) 0.300

iii) 0.76

iv) 0.704

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  $261.50 per month

Standard Deviation, σ = $16.25

We are given that the distribution of monthly food  cost for a 14- to 18-year-old male is a bell shaped distribution that is a normal distribution.

Formula:

a) P(Less than $280)

Calculation the value from standard normal z table, we have,  

b) P(More than $270)

P(x > 270)

Calculation the value from standard normal z table, we have,  

c) P(More than $250)

P(x > 250)

Calculation the value from standard normal z table, we have,  

d) P(Between $240 and $275)

e) Thus, 0.704 is the probability  that the monthly food cost for a randomly selected 14- to 18-year-old male is between $240 and $275.

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step-by-step explanation: