If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?

A) 71.76
B) 67.96
C) 61.96
D) 48.24
E) 54.99

Question

christian alvarez · Accepted Answer

Final Answer : A, Explanation :   The z-score formula is   z = x − μ σ z = \frac{x - \mu}{\sigma} z = σ x − μ ​  , where   x x x   is the value,   μ \mu μ   is the mean, and   σ \sigma σ   is the standard deviation. Plugging in the given values:   1.96 = x − 60 6 1.96 = \frac{x - 60}{6} 1.96 = 6 x − 60 ​  . Solving for   x x x   gives   x = 1.96 × 6 + 60 = 11.76 + 60 = 71.76 x = 1.96 	imes 6 + 60 = 11.76 + 60 = 71.76 x = 1.96 × 6 + 60 = 11.76 + 60 = 71.76  .

If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?

A) 71.76
B) 67.96
C) 61.96
D) 48.24
E) 54.99

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If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?A) 71.76B) 67.96C) 61.96D) 48.24E) 54.99

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Learning Objectives

Learning Objectives

Related questions

If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?

A) 71.76
B) 67.96
C) 61.96
D) 48.24
E) 54.99