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masha68 [24]
3 years ago
6

A standardized test has a mean of 110 points and a standard deviation of 10 points. John scored at the 98th percentile on the te

st. Find his score to the nearest whole number.
Mathematics
1 answer:
Mariana [72]3 years ago
4 0

Answer: his score 131 points

Step-by-step explanation:

Assuming the scores in the standardized test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = standardized test scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 110 points

σ = 10 points

Looking at the normal distribution table, the z score that corresponds to the 98 percentile is 2.06

2.06 = (x - 110)/10

Cross multiplying, it becomes

2.06 × 10 = x - 110

2.06 = x - 110

x = 20.6 + 110

x = 130.6

Approximately, x = 131

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Step-by-step explanation:

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(0,-4),(1,0),(2,2) find a quadratic function in standard form for each set of points.
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Steven is walking around the perimeter of a circular swimming pool
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2 years ago
Read 2 more answers
For a data set of the pulse rates for a sample of adult? females, the lowest pulse rate is 39 beats per? minute, the mean of the
Zarrin [17]

Answer:

a) The difference is of 35 beats per minute.

b) So 3.07 standard deviations below the mean.

c) Z = -3.07.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean \mu = 74, standard deviation \sigma = 11.4

a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the? females?

39 - 74 = -35

The difference is of 35 beats per minute.

b. How many standard deviations is that? [the difference found in part? (a)?

|Z| when X = 39. So

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

Z = \frac{39 - 74}{11.4}

Z = -3.07

|Z| = 3.07

So 3.07 standard deviations below the mean.

c. Convert the pulse rate of 39 beats per minutes to a z score.

From item b. above, Z = -3.07.

5 0
2 years ago
You need to rent a video camera for your school project. Murphy's Camera charges a $30 rental fee plus $35 per day. Allied Renta
andreev551 [17]

A. If a camera is rented for 1 or 2 days, it would be logical to rent it from Murphy's.

B. If a camera is needed for more than 3 days, it would make sense to rent it from Allied rental.

C. Yes, if a camera is rented for 3 days both rentals charge the same money.

C. If you were need a camera for 3 days, you would have to pay $135 for both stores.

<u>Step-by-step explanation:</u>

Step 1; Murphy's camera costs $30 to rent and an additional $35 for each day of rental. So the equations are

y = $30 + (x × $35), where y is total cost and x is the number of days rented.

So for x = 1, y = $30 + (1 × $35) = $30 + $35 = $65

So for x = 2, y = $30 + (2 × $35) = $30 + $70 = $100

So for x = 3, y = $30 + (3 × $35) = $30 + $105 = $135

So for x = 4, y = $30 + (4 × $35) = $30 + $140 = $170

So for x = 5, y = $30 + (5 × $35) = $30 + $175 = $ 205.

Step 2; Allied rental costs $45 to rent and a $30 for each day of rental. So the equations are as follows

y = $45 + (x × $30), where y is total cost and x is the days rented

So for x = 1, $45 + (1 × $30) = $45 + $30 = $75

So for x = 2, $45 + (2 × $30) = $45 + $60 = $105

So for x = 3, $45 + (3 × $30) = $45 + $90 = $135

So for x = 4, $45 + (4 × $30) = $45 + $120 = $165

So for x = 5, $45 + (5 × $30) = $45 + $150 = $195

Step 3; Comparing both prices over 5 days. Murphy's is cheaper for until 2 days. On day 3 both the rentals cost the same but after day 4, allied rentals is the better option.

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3 years ago
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