Question

Assume the random variable X is normally distributed with mean u=55 and standard deviation sigmaσequals=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. ​P(48 ≤X ≤67​). HOW TO ENTER IT IN TI 83

Answer 1

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1. To compute the probability by hand here' the answer:

P(48<=X<=67)

= P( 48-55/7 <= Z<= 67-55/7) [we used Z tables to convert Z values into probabilities]

= P(-1<=Z<=1.7143)

= 0.9568- 0.1587

= 0.7981

Here are the steps on TI 83 calculator. I have drawn the graph below the steps :

2.

Press 2nd VARS [DISTR].

2. Scroll down to 2:normalcdf(

3. Press ENTER.

4. Enter 48,67,55,7)

5. and press ENTER to get the answer . The syntax is normalcdf(smaller, larger, µ, σ).

Answer should come out to be: 0.7981

3. The normal distribution with shaded area and all relevant marking are below: