Question

Using the mean and the standard deviation you found in the second question​ (rounded to four​ decimals), answer the following probability questions using​ Stat>Calculators>Normal.

For​ each, copy and paste the StatCrunch output in the SHOW YOUR WORK.

Here is a short video that shows how to insert multiple graphs into the SHOW WORK​ area:

SHOW WORK

1. What is the probability that a randomly selected​ 5-year-old female will be taller than 40 inches​ tall? (Round to 4 decimal​ places)  

2. What is the probability that a randomly selected​ 5-year-old female will be shorter than 35 inches​ tall? (Round to 4 decimal​ places)

3. What is the probability that a randomly selected​ 5-year-old female will be between 39 and 47 inches​ tall? ​ (Round to 4 decimal​ places)

This is Question 2

44.5	42.4	42.2	46.2	45.7	44.8	43.3	39.5	45.4	43.0
43.4	44.7	38.6	41.6	50.2	46.9	39.6	44.7	36.5	42.7
40.6	47.5	48.4	37.5	45.5	43.3	41.2	40.5	44.4	42.6
42.0	40.3	42.0	42.2	38.5	43.6	40.6	45.0	40.7	36.3
44.5	37.6	42.2	40.3	48.5	41.6	41.7	38.9	39.5	43.6
41.3	38.8	41.9	40.3	42.1	41.9	42.3	44.6	40.5	37.4
44.5	40.7	38.2	42.6	44.0	35.9	43.7	48.1	38.7	46.0
43.4	44.6	37.7	34.6	42.4	42.7	47.0	42.8	39.9	42.3

Mean 42.2238

standard​ deviation 3.131

Answer 1

Given: u = 42.2238, = 3.131

We have, z = (x-u)/

1. What is the probability that a randomly selected​ 5-year-old female will be taller than 40 inches​ tall? (Round to 4 decimal​ places)  

= P(x > 40)

= P(z > (40-42.2238)/3.131)

= P(z > -0.710)

= 0.7611

2. What is the probability that a randomly selected​ 5-year-old female will be shorter than 35 inches​ tall? (Round to 4 decimal​ places)

= P(x < 35)

= P(z < (35-42.2238)/3.131)

= P(z < -2.307)

= 0.0105

3. What is the probability that a randomly selected​ 5-year-old female will be between 39 and 47 inches​ tall? ​ (Round to 4 decimal​ places)

= P(39 < x < 47)

= P((39-42.2238)/3.131 < z < (47-42.2238)/3.131)

= P(-1.030 < z < 1.525)

= P(z < 1.525) - P(z < -1.030)

= 0.9364 - 0.1515

= 0.7849