SOLUTION: According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose o

Question 1199362: According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(64, 2.3)
b. Find the probability that the person is between 61.9 and 63.3 inches.
0.1998
c. The middle 20% of Martian heights lie between what two numbers?
Low:
inches
High:
inches
How do I solve letter C?
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.

Middle 20% are those who are lower than upper 60% and higher than lower 40%.

Use your calculator TI-83 or TI-84 with function   invNorm.
Its format is   p = invNorm ( probability, mu, SD).

For details and instructions about this function and how to use it, see web-site
https://www.statology.org/invnorm-ti-84/

The z-scores are

        z_lower_40% = invNorm(0.4, 64, 2.3) = 63.4173.

        z_upper_60% = invNorm(0.6, 64, 2.3) = 64.5827.

ANSWER.     The middle 20% of Martian heights lie between 63.42 and 64.58 inches   (after rounding).

-------------------

You may also use online calculator https://onlinestatbook.com/2/calculators/inverse_normal_dist.html

It has several advantages:

        - it is free of charge;
        - it has simple and intuitively clear interface, and
        - it shows you the shaded area of interest, so at any time moment you can see and understand
              what you are doing, what you are doing wrong (if any) and how to do it right.

Play with this online calculator and use it in different modes until everything will become clear to you.

This online calculator is the best tool to learn about the normal distribution
and to learn on how to work with normal distribution, making necessary calculations.

So, this online calculator is your best teacher, best assistant and your
best friend when you calculate something related to normal distribution.

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