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ASHA 777 [7]
3 years ago
12

In a recent contest, the mean score was 210 and the standard deviation was 25. a) Find the z-score of John who scored 190 b) Fin

d the z-score of Bill who scored 270 c) If Mary had a score of 1.25, what was Mary’s score?
Mathematics
2 answers:
UNO [17]3 years ago
8 0

Answer:

Step-by-step explanation:

The formula for normal distribution is expressed as

z = (x - µ)/σ

Where

x = scores in the contest.

µ = mean score.

σ = standard deviation

From the information given,

µ = 210

σ = 25

a) The z-score of John who scored 190

z = (190 - 210)/25 = - 20/25 = - 0.8

b) The z-score of Bill who scored 270

z = (270 - 210)/25 = 60/25 = 2.4

c) If Mary had a score of 1.25, what was Mary’s score,

1.25 = (x - 210)/25

Cross multiplying,

25 × 1.25 = x - 210

x = 31.25 + 210 = 241.25

Mary's score is 241.25

denpristay [2]3 years ago
3 0

Answer:

a) Z = -0.8

b) Z = 2.4

c) Mary's score was 241.25.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 210, \sigma = 25

a) Find the z-score of John who scored 190

Z = \frac{X - \mu}{\sigma}

Z = \frac{190 - 210}{25}

Z = -0.8

b) Find the z-score of Bill who scored 270

Z = \frac{X - \mu}{\sigma}

Z = \frac{270 - 210}{25}

Z = 2.4

c) If Mary had a score of 1.25, what was Mary’s score?

Z = \frac{X - \mu}{\sigma}

1.25 = \frac{X - 210}{25}

X - 210 = 25*1.25

X = 241.25

Mary's score was 241.25.

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