Question

Supposed normal distribution has a mean of 89 and a standard deviation of 7. What is P(x≤82)? NO LINKS!!!

a. 0.975
b. 0.84
c. 0.16
d. 0.025​

Answer 1

• Mean=
  `\overline{x}`=89
• Standard deviation=
  `\sum`=7

• x is 82

z value:-

`\\ \rm\Rrightarrow \frac{x-\overline{x}}{\sum}`

`\\ \rm\Rrightarrow (82-89)/(7)`

`\\ \rm\Rrightarrow (-7)/(7)`

`\\ \rm\Rrightarrow -1`

• z=-1

As per z value chart

• Part distributed to z=-1 is 32%/2=16%=0.16

Option C is correct

Answer 2

Answer: C) 0.16

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Step-by-step explanation:

Convert the x = 82 to a corresponding z score.

z = (x-mu)/sigma

z = (82 - 89)/7

z = -7/7

z = -1

Using the empirical rule (see chart below), roughly 68% of the distribution is within 1 standard deviation of the mean.

This leaves 1 - 0.68 = 0.32 = 32% of the distribution in both tails, and (32%)/2 = 16% of the area is in one tail, which converts to 0.16

About 16% of the normally distributed population is below z = -1.

So we can say
`P(x \le 82) = P(z \le -1) \approx 0.16`