Question

What is the probability that a data value in a normal distribution is between a

Z-score of -0.41 and a z-score of 1.25? Round your answer to the nearest
tenth of a percent
O A. 55.3%
OB. 84.3%
O c. 46.2%
O D. 65.0%

Answer 1

Answer: choice A) 55.3%

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Step-by-step explanation:

Use a Z table found in the back of your book to find that

P(Z < -0.41) = 0.3409

P(Z < 1.25) = 0.8944

So,

P(-0.41 < Z < 1.25) = P(Z < 1.25) - P(Z < -0.41)

P(-0.41 < Z < 1.25) = 0.8944 - 0.3409

P(-0.41 < Z < 1.25) = 0.5535

Now convert this to a percentage by multiplying by 100, which is the same as moving the decimal point over 2 places

0.5535 ---> 55.35%

Round this to the nearest tenth of a percent. You could argue that 55.35% rounds to either 55.3% or 55.4% since that last digit is a 5. I'm going with 55.3% since 55.4% isn't listed as an answer choice. The table I used only lists approximate values, so there is likely some rounding error somewhere. When I used my TI83 (see image below) I got roughly 0.5534 which is fairly close to 0.5535. If you want to use your TI83 or TI84 calculator, then the normalcdf function can be found by pressing the yellow "2ND" button (top left corner) and then pressing the VARS key (3rd row from the top, just to the left of the CLEAR key).