Question

please answer all

1.) Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis. (Round your answers to two decimal places.)

(a) The point z with 64% of the observations falling below it

z =

(b) The point z with 20% of the observations falling above it

2.)Suppose a normal distribution has a mean of five and a standard deviation of 1.75. What is the z-score of

x = 3.5?

(Round your answer to two decimal places.)

3.)The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.9 days and a standard deviation of 2.5 days.

What is the 75th percentile for recovery times? (Round your answer to two decimal places.)
days

Answer 1

Q 1) The point z with 64% of the observations falling below it

Therefore, from standard normal table, the area value of z corresponding to the are 0.14 is 0.358

b) The point z with 20% of the observations falling above it

From Standard normal table, the value of z corresponding to the area 0.30 is 0.841

Q 2) X ~ N(5, 1.75)

when X = 3.5, the Z score is

Q3) Let X be the  patient recovery time

X ~N( 5.9, 2.5)

For 75th percentile the critical value of Z is 0.674

The value of Z corresponding to the area 0.25 (from standard normal table ) is 0.674

Therefore the 75th percentile for recovery times is