Question

Assume that the random variable X is normally distributed, with mean 48 and standard deviation = 9. Compute the probability Be sure to draw a normal curve with the area corresponding to the probability shaded. PIX S40) Which of the following shaded regions corresponds to PIX S4072 B. OA. @ 4048 4048 40 40 POX540)- (Round to four decimal places as needed Click to select your answer(s)

Answer 1

Given Mean $\mu$ = 48

Standard Deviation $\sigma$ = 9

We need to find P(X $\leq$ 40)

z-score = (X - $\mu$ ) /  $\sigma$

= (40 - 48) / 9

= -8 / 9

= -0.88889

The area to the left of z-score will give us P(X $\leq$ 40) which is 0.1870314 from online calculator since the z-tables wont give us the exact area

So  P(X $\leq$ 40) = 0.1870314

= 0.1870 rounded to four decimal places

The normal curve will be similar to one in option B since Mean 48 wil be at the centre and 40 will be to the left of it and the shaded region should be less than or equal to 40

So Answer is Option B