Question

The heights (in inches) of 40 people are recorded.

Mean	64.325
Std Dev	4.1099473
Std Err Mean	0.6498397
Upper 95% Mean	65.639425
Lower 95% Mean	63.010575
N	40

• (a)

  How many people are shorter than 70 inches?

  What proportion (as a decimal) of the total number of people is this?

• (b)

  How many people are taller than 65 inches?

  What proportion (as a decimal) of the total number of people is this?

• (c)

  How many people are between 60 inches and 70 inches?

  What proportion (as a decimal) of the total number of people is this?

• (d)

  Is the shape of the distribution of heights symmetric, positively skewed, or negatively skewed?

  symmetricpositively skewed    negatively skewed

Answer 1

This is a normal distribution question with

a) x = 70

P(x < 70.0)=?

The z-score at x = 70.0 is,

z = 1.3808

This implies that

b) x = 65

P(x > 65.0)=?

The z-score at x = 65.0 is,

z = 0.1642

This implies that

P(x > 65.0) = P(z > 0.1642) = 1 - 0.5652131494464501

c)

P(60.0 < x < 70.0)=?

This implies that

P(60.0 < x < 70.0) = P(-1.0523 < z < 1.3808) = P(Z < 1.3808) - P(Z < -1.0523)

P(60.0 < x < 70.0) = 0.9163297682427174 - 0.14633096584418198

d)

Since, this is a normal distribution question with so the shape of distribution in symmetric

PS: you have to refer z score table to find the final probabilities.

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