For rldiuion verfy that the probb rounded to two decimal places) within b. 0 85

Question

For rldiuion verfy that the probb rounded to two decimal places) within b. 0 85 standard deviations of the mean equals 0.60 c. Find the probability that falls within 0.43 standard deviations of the mean. d. Sketch these three cases on a single graph Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. a. Choose the correct response from the following O A. Looking up 2 12 in a standard normal distribution table, the cumulative probability is 0 9830 Likewise, the cumulative probablit is 0 0170 for -2.12 O B. Looking up 2.12 in a standard normal distribution table, the cumulative probability is 0 0170 C. Looking up 2 12 in a standard normal distribution table the cumulative probabil y s 09660 which rounds to 97 0 9830-0 0170-0 9660, which rounds to 0 97 . The cumulative probability is 0 9830 for 212 0 9830-070-0 9660, which rounds to 0 97 b. Choose the correct response from the following A By a standard normal distribution table, the cumulative probability to the left of 0 85 is 0 8023 The cumulative probability to the right of-085 s 0.1977 0 8023-0 1977-0 6046 which founds to 060 O B. By a standard normal distribution table, the cumulative probability to the left of - 0.85 is 0.6046, which rounds to 0.60 C By a standard normal distribution table, the cumulative probability to the left of 0 85 is 0 8023 The cumulative probability to the left of-0.85 is 0 1978023-0 1977:06046. hich dst 60. C. The probability that falls within 0 43 standard deviations of the mean is (Round to two decimal places as needed) d. Choose the correct graph from the following B. O C. A.

Explanation / Answer

a) The correct option is A)

Standard normal table (z table) gives less than probabilities from the given values.

Here we want to find P( -2.12 < Z < 2.12) = P( Z < 2.12) - P(Z < -2.12)

From s tandard normal table   P( Z < 2.12) = 0.9830  

and P( Z < - 2.12 ) = 0.0170

so that  P( -2.12 < Z < 2.12) = 0.9830 -   0.0170 = 0.9660 = 0.97 (after rounding)

b) the correct option is C)

Because standard normal table gives left area from the given value.

c) In this part we need to find P( - 0.43 < Z < 0.43) = P( Z < 0.43) - P( Z < -0.43)

From standard normal table P( Z < 0.43) = 0.6664

and P(Z < -0.43) = 0.3336

so that   P( - 0.43 < Z < 0.43) =  0.6664 -  0.3336 = 0.3328 = 0.33 ( after rounding)

d) the correct option is A

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