Question

Solve the following:
1.
An amount of purchase of a customer in a mall of a city follows normal distribution
mean 800 and standard deviation 200. If a customer is selected at random then
the probabilities for the following events :
(1) Amount of purchase made by him is in between 850 to 1200.
(2) Amount of purchase made by him is in between 600 to 750.
20 vears and 26 years of certain aru​

Answer 1

Answer:

Recognize the normal probability distribution and apply it appropriately.

Compare normal probabilities by converting to the standard normal distribution.

EXAMPLE

The shaded area in the following graph indicates the area to the left of

x. This area is represented by the probability P(X < x). Normal tables, computers, and calculators provide or calculate the probability P(X < x).

Note

To calculate the probability without the use of technology, use the probability tables provided here. The tables include instructions for how to use them.

If the area to the left is 0.0228, then the area to the right is 1 – 0.0228 = 0.9772.

TRY IT

If the area to the left of x is 0.012, then what is the area to the right?

1 − 0.012 = 0.988

EXAMPLE

The final exam scores in a statistics class were normally distributed with a mean of 63 and a standard deviation of five.

Find the probability that a randomly selected student scored more than 65 on the exam.

Find the probability that a randomly selected student scored less than 85.

Find the 90th percentile (that is, find the score k that has 90% of the scores below k and 10% of the scores above k).

Find the 70th percentile (that is, find the score k such that 70% of scores are below k and 30% of the scores are above k).

Solution:

LetX = a score on the final exam. X ~ N(63, 5), where μ = 63 and σ = 5

Draw a graph. Then, find P(x > 65). P(x > 65) = 0.3446

Step-by-step explanation: